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r_{k+1}",[573,996,998,1081,1140,1196],{"className":997,"ariaHidden":598},[611],[573,999,1001,1005,1072,1075,1078],{"className":1000},[615],[573,1002],{"className":1003,"style":1004},[619],"height:0.6389em;vertical-align:-0.2083em;",[573,1006,1008,1012],{"className":1007},[624],[573,1009,948],{"className":1010,"style":1011},[624,625],"margin-right:0.0278em;",[573,1013,1016],{"className":1014},[1015],"msupsub",[573,1017,1021,1063],{"className":1018},[1019,1020],"vlist-t","vlist-t2",[573,1022,1025,1058],{"className":1023},[1024],"vlist-r",[573,1026,1030],{"className":1027,"style":1029},[1028],"vlist","height:0.3361em;",[573,1031,1033,1038],{"style":1032},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[573,1034],{"className":1035,"style":1037},[1036],"pstrut","height:2.7em;",[573,1039,1045],{"className":1040},[1041,1042,1043,1044],"sizing","reset-size6","size3","mtight",[573,1046,1048,1052,1055],{"className":1047},[624,1044],[573,1049,953],{"className":1050,"style":1051},[624,625,1044],"margin-right:0.0315em;",[573,1053,956],{"className":1054},[805,1044],[573,1056,960],{"className":1057},[624,1044],[573,1059,1062],{"className":1060},[1061],"vlist-s","​",[573,1064,1066],{"className":1065},[1024],[573,1067,1070],{"className":1068,"style":1069},[1028],"height:0.2083em;",[573,1071],{},[573,1073],{"className":1074,"style":780},[633],[573,1076,719],{"className":1077},[784],[573,1079],{"className":1080,"style":780},[633],[573,1082,1084,1088,1131,1134,1137],{"className":1083},[615],[573,1085],{"className":1086,"style":1087},[619],"height:0.6389em;vertical-align:-0.1944em;",[573,1089,1091,1095],{"className":1090},[624],[573,1092,967],{"className":1093,"style":1094},[624,625],"margin-right:0.0359em;",[573,1096,1098],{"className":1097},[1015],[573,1099,1101,1122],{"className":1100},[1019,1020],[573,1102,1104,1119],{"className":1103},[1024],[573,1105,1107],{"className":1106,"style":1029},[1028],[573,1108,1110,1113],{"style":1109},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[573,1111],{"className":1112,"style":1037},[1036],[573,1114,1116],{"className":1115},[1041,1042,1043,1044],[573,1117,953],{"className":1118,"style":1051},[624,625,1044],[573,1120,1062],{"className":1121},[1061],[573,1123,1125],{"className":1124},[1024],[573,1126,1129],{"className":1127,"style":1128},[1028],"height:0.15em;",[573,1130],{},[573,1132],{"className":1133,"style":801},[633],[573,1135,724],{"className":1136},[805],[573,1138],{"className":1139,"style":801},[633],[573,1141,1143,1147,1187,1190,1193],{"className":1142},[615],[573,1144],{"className":1145,"style":1146},[619],"height:0.7333em;vertical-align:-0.15em;",[573,1148,1150,1153],{"className":1149},[624],[573,1151,948],{"className":1152,"style":1011},[624,625],[573,1154,1156],{"className":1155},[1015],[573,1157,1159,1179],{"className":1158},[1019,1020],[573,1160,1162,1176],{"className":1161},[1024],[573,1163,1165],{"className":1164,"style":1029},[1028],[573,1166,1167,1170],{"style":1032},[573,1168],{"className":1169,"style":1037},[1036],[573,1171,1173],{"className":1172},[1041,1042,1043,1044],[573,1174,953],{"className":1175,"style":1051},[624,625,1044],[573,1177,1062],{"className":1178},[1061],[573,1180,1182],{"className":1181},[1024],[573,1183,1185],{"className":1184,"style":1128},[1028],[573,1186],{},[573,1188],{"className":1189,"style":801},[633],[573,1191,729],{"className":1192},[805],[573,1194],{"className":1195,"style":801},[633],[573,1197,1199,1202],{"className":1198},[615],[573,1200],{"className":1201,"style":1004},[619],[573,1203,1205,1208],{"className":1204},[624],[573,1206,948],{"className":1207,"style":1011},[624,625],[573,1209,1211],{"className":1210},[1015],[573,1212,1214,1243],{"className":1213},[1019,1020],[573,1215,1217,1240],{"className":1216},[1024],[573,1218,1220],{"className":1219,"style":1029},[1028],[573,1221,1222,1225],{"style":1032},[573,1223],{"className":1224,"style":1037},[1036],[573,1226,1228],{"className":1227},[1041,1042,1043,1044],[573,1229,1231,1234,1237],{"className":1230},[624,1044],[573,1232,953],{"className":1233,"style":1051},[624,625,1044],[573,1235,729],{"className":1236},[805,1044],[573,1238,960],{"className":1239},[624,1044],[573,1241,1062],{"className":1242},[1061],[573,1244,1246],{"className":1245},[1024],[573,1247,1249],{"className":1248,"style":1069},[1028],[573,1250],{}," notieren.",[928,1253,1254],{},"Die vorletzte Gleichung nach dem ggT auflösen.",[928,1256,1257,1258,891,1286,1314],{},"Von unten nach oben die Reste nacheinander durch die darüberliegenden Gleichungen ersetzen, bis nur noch ",[573,1259,1261,1274],{"className":1260},[576],[573,1262,1264],{"className":1263},[580],[582,1265,1266],{"xmlns":584},[586,1267,1268,1272],{},[589,1269,1270],{},[592,1271,594],{},[604,1273,594],{"encoding":606},[573,1275,1277],{"className":1276,"ariaHidden":598},[611],[573,1278,1280,1283],{"className":1279},[615],[573,1281],{"className":1282,"style":887},[619],[573,1284,594],{"className":1285},[624,625],[573,1287,1289,1302],{"className":1288},[576],[573,1290,1292],{"className":1291},[580],[582,1293,1294],{"xmlns":584},[586,1295,1296,1300],{},[589,1297,1298],{},[592,1299,602],{},[604,1301,602],{"encoding":606},[573,1303,1305],{"className":1304,"ariaHidden":598},[611],[573,1306,1308,1311],{"className":1307},[615],[573,1309],{"className":1310,"style":853},[619],[573,1312,602],{"className":1313},[624,625]," vorkommen.",[565,1316,1317,1318,1403,1404,1755,1756,1784],{},"Die Koeffizienten sind nicht eindeutig: Mit ",[573,1319,1321,1352],{"className":1320},[576],[573,1322,1324],{"className":1323},[580],[582,1325,1326],{"xmlns":584},[586,1327,1328,1349],{},[589,1329,1330,1333,1335,1337,1339,1341,1343,1345,1347],{},[592,1331,1332],{},"d",[596,1334,719],{},[592,1336,700],{"mathvariant":699},[596,1338,703],{},[596,1340,707],{"stretchy":706},[592,1342,594],{},[596,1344,599],{"separator":598},[592,1346,602],{},[596,1348,716],{"stretchy":706},[604,1350,1351],{"encoding":606},"d = \\operatorname{ggT}(a, b)",[573,1353,1355,1373],{"className":1354,"ariaHidden":598},[611],[573,1356,1358,1361,1364,1367,1370],{"className":1357},[615],[573,1359],{"className":1360,"style":853},[619],[573,1362,1332],{"className":1363},[624,625],[573,1365],{"className":1366,"style":780},[633],[573,1368,719],{"className":1369},[784],[573,1371],{"className":1372,"style":780},[633],[573,1374,1376,1379,1385,1388,1391,1394,1397,1400],{"className":1375},[615],[573,1377],{"className":1378,"style":748},[619],[573,1380,1382],{"className":1381},[752],[573,1383,700],{"className":1384},[624,756],[573,1386,707],{"className":1387},[760],[573,1389,594],{"className":1390},[624,625],[573,1392,599],{"className":1393},[629],[573,1395],{"className":1396,"style":634},[633],[573,1398,602],{"className":1399},[624,625],[573,1401,716],{"className":1402},[776]," ist auch ",[573,1405,1407,1470],{"className":1406},[576],[573,1408,1410],{"className":1409},[580],[582,1411,1412],{"xmlns":584},[586,1413,1414,1467],{},[589,1415,1416,1437,1439,1441,1461,1463,1465],{},[589,1417,1418,1420,1422,1424,1426,1428,1435],{},[596,1419,707],{"fence":598},[592,1421,653],{},[596,1423,729],{},[592,1425,953],{},[596,1427,724],{},[1429,1430,1431,1433],"mfrac",{},[592,1432,602],{},[592,1434,1332],{},[596,1436,716],{"fence":598},[592,1438,594],{},[596,1440,729],{},[589,1442,1443,1445,1447,1449,1451,1453,1459],{},[596,1444,707],{"fence":598},[592,1446,658],{},[596,1448,956],{},[592,1450,953],{},[596,1452,724],{},[1429,1454,1455,1457],{},[592,1456,594],{},[592,1458,1332],{},[596,1460,716],{"fence":598},[592,1462,602],{},[596,1464,719],{},[592,1466,1332],{},[604,1468,1469],{"encoding":606},"\\left(s + k \\cdot \\frac{b}{d}\\right) a + \\left(t - k \\cdot \\frac{a}{d}\\right) b = d",[573,1471,1473,1616,1746],{"className":1472,"ariaHidden":598},[611],[573,1474,1476,1480,1601,1604,1607,1610,1613],{"className":1475},[615],[573,1477],{"className":1478,"style":1479},[619],"height:1.2301em;vertical-align:-0.35em;",[573,1481,1484,1494,1497,1500,1503,1506,1509,1512,1515,1518,1595],{"className":1482},[1483],"minner",[573,1485,1489],{"className":1486,"style":1488},[760,1487],"delimcenter","top:0em;",[573,1490,707],{"className":1491},[1492,1493],"delimsizing","size1",[573,1495,653],{"className":1496},[624,625],[573,1498],{"className":1499,"style":801},[633],[573,1501,729],{"className":1502},[805],[573,1504],{"className":1505,"style":801},[633],[573,1507,953],{"className":1508,"style":1051},[624,625],[573,1510],{"className":1511,"style":801},[633],[573,1513,724],{"className":1514},[805],[573,1516],{"className":1517,"style":801},[633],[573,1519,1521,1525,1592],{"className":1520},[624],[573,1522],{"className":1523},[760,1524],"nulldelimiter",[573,1526,1528],{"className":1527},[1429],[573,1529,1531,1583],{"className":1530},[1019,1020],[573,1532,1534,1580],{"className":1533},[1024],[573,1535,1538,1554,1565],{"className":1536,"style":1537},[1028],"height:0.8801em;",[573,1539,1541,1545],{"style":1540},"top:-2.655em;",[573,1542],{"className":1543,"style":1544},[1036],"height:3em;",[573,1546,1548],{"className":1547},[1041,1042,1043,1044],[573,1549,1551],{"className":1550},[624,1044],[573,1552,1332],{"className":1553},[624,625,1044],[573,1555,1557,1560],{"style":1556},"top:-3.23em;",[573,1558],{"className":1559,"style":1544},[1036],[573,1561],{"className":1562,"style":1564},[1563],"frac-line","border-bottom-width:0.04em;",[573,1566,1568,1571],{"style":1567},"top:-3.394em;",[573,1569],{"className":1570,"style":1544},[1036],[573,1572,1574],{"className":1573},[1041,1042,1043,1044],[573,1575,1577],{"className":1576},[624,1044],[573,1578,602],{"className":1579},[624,625,1044],[573,1581,1062],{"className":1582},[1061],[573,1584,1586],{"className":1585},[1024],[573,1587,1590],{"className":1588,"style":1589},[1028],"height:0.345em;",[573,1591],{},[573,1593],{"className":1594},[776,1524],[573,1596,1598],{"className":1597,"style":1488},[776,1487],[573,1599,716],{"className":1600},[1492,1493],[573,1602],{"className":1603,"style":634},[633],[573,1605,594],{"className":1606},[624,625],[573,1608],{"className":1609,"style":801},[633],[573,1611,729],{"className":1612},[805],[573,1614],{"className":1615,"style":801},[633],[573,1617,1619,1623,1731,1734,1737,1740,1743],{"className":1618},[615],[573,1620],{"className":1621,"style":1622},[619],"height:1.2em;vertical-align:-0.35em;",[573,1624,1626,1632,1635,1638,1641,1644,1647,1650,1653,1656,1725],{"className":1625},[1483],[573,1627,1629],{"className":1628,"style":1488},[760,1487],[573,1630,707],{"className":1631},[1492,1493],[573,1633,658],{"className":1634},[624,625],[573,1636],{"className":1637,"style":801},[633],[573,1639,956],{"className":1640},[805],[573,1642],{"className":1643,"style":801},[633],[573,1645,953],{"className":1646,"style":1051},[624,625],[573,1648],{"className":1649,"style":801},[633],[573,1651,724],{"className":1652},[805],[573,1654],{"className":1655,"style":801},[633],[573,1657,1659,1662,1722],{"className":1658},[624],[573,1660],{"className":1661},[760,1524],[573,1663,1665],{"className":1664},[1429],[573,1666,1668,1714],{"className":1667},[1019,1020],[573,1669,1671,1711],{"className":1670},[1024],[573,1672,1675,1689,1697],{"className":1673,"style":1674},[1028],"height:0.6954em;",[573,1676,1677,1680],{"style":1540},[573,1678],{"className":1679,"style":1544},[1036],[573,1681,1683],{"className":1682},[1041,1042,1043,1044],[573,1684,1686],{"className":1685},[624,1044],[573,1687,1332],{"className":1688},[624,625,1044],[573,1690,1691,1694],{"style":1556},[573,1692],{"className":1693,"style":1544},[1036],[573,1695],{"className":1696,"style":1564},[1563],[573,1698,1699,1702],{"style":1567},[573,1700],{"className":1701,"style":1544},[1036],[573,1703,1705],{"className":1704},[1041,1042,1043,1044],[573,1706,1708],{"className":1707},[624,1044],[573,1709,594],{"className":1710},[624,625,1044],[573,1712,1062],{"className":1713},[1061],[573,1715,1717],{"className":1716},[1024],[573,1718,1720],{"className":1719,"style":1589},[1028],[573,1721],{},[573,1723],{"className":1724},[776,1524],[573,1726,1728],{"className":1727,"style":1488},[776,1487],[573,1729,716],{"className":1730},[1492,1493],[573,1732],{"className":1733,"style":634},[633],[573,1735,602],{"className":1736},[624,625],[573,1738],{"className":1739,"style":780},[633],[573,1741,719],{"className":1742},[784],[573,1744],{"className":1745,"style":780},[633],[573,1747,1749,1752],{"className":1748},[615],[573,1750],{"className":1751,"style":853},[619],[573,1753,1332],{"className":1754},[624,625]," für jedes ganze ",[573,1757,1759,1772],{"className":1758},[576],[573,1760,1762],{"className":1761},[580],[582,1763,1764],{"xmlns":584},[586,1765,1766,1770],{},[589,1767,1768],{},[592,1769,953],{},[604,1771,953],{"encoding":606},[573,1773,1775],{"className":1774,"ariaHidden":598},[611],[573,1776,1778,1781],{"className":1777},[615],[573,1779],{"className":1780,"style":853},[619],[573,1782,953],{"className":1783,"style":1051},[624,625],".",[565,1786,1787,1788,1791,1792,1878,1879,1996,1997,2132,2133,2161,2162,2245,2246,2274,2275,2303],{},"Wichtigste Anwendung ist das ",[569,1789,1790],{},"modulare Inverse",": Ist ",[573,1793,1795,1826],{"className":1794},[576],[573,1796,1798],{"className":1797},[580],[582,1799,1800],{"xmlns":584},[586,1801,1802,1823],{},[589,1803,1804,1806,1808,1810,1812,1814,1817,1819,1821],{},[592,1805,700],{"mathvariant":699},[596,1807,703],{},[596,1809,707],{"stretchy":706},[592,1811,594],{},[596,1813,599],{"separator":598},[592,1815,1816],{},"m",[596,1818,716],{"stretchy":706},[596,1820,719],{},[958,1822,960],{},[604,1824,1825],{"encoding":606},"\\operatorname{ggT}(a, m) = 1",[573,1827,1829,1868],{"className":1828,"ariaHidden":598},[611],[573,1830,1832,1835,1841,1844,1847,1850,1853,1856,1859,1862,1865],{"className":1831},[615],[573,1833],{"className":1834,"style":748},[619],[573,1836,1838],{"className":1837},[752],[573,1839,700],{"className":1840},[624,756],[573,1842,707],{"className":1843},[760],[573,1845,594],{"className":1846},[624,625],[573,1848,599],{"className":1849},[629],[573,1851],{"className":1852,"style":634},[633],[573,1854,1816],{"className":1855},[624,625],[573,1857,716],{"className":1858},[776],[573,1860],{"className":1861,"style":780},[633],[573,1863,719],{"className":1864},[784],[573,1866],{"className":1867,"style":780},[633],[573,1869,1871,1875],{"className":1870},[615],[573,1872],{"className":1873,"style":1874},[619],"height:0.6444em;",[573,1876,960],{"className":1877},[624],", dann folgt aus ",[573,1880,1882,1912],{"className":1881},[576],[573,1883,1885],{"className":1884},[580],[582,1886,1887],{"xmlns":584},[586,1888,1889,1909],{},[589,1890,1891,1893,1895,1897,1899,1901,1903,1905,1907],{},[958,1892,960],{},[596,1894,719],{},[592,1896,653],{},[596,1898,724],{},[592,1900,594],{},[596,1902,729],{},[592,1904,658],{},[596,1906,724],{},[592,1908,1816],{},[604,1910,1911],{"encoding":606},"1 = s \\cdot a + t \\cdot m",[573,1913,1915,1933,1951,1969,1987],{"className":1914,"ariaHidden":598},[611],[573,1916,1918,1921,1924,1927,1930],{"className":1917},[615],[573,1919],{"className":1920,"style":1874},[619],[573,1922,960],{"className":1923},[624],[573,1925],{"className":1926,"style":780},[633],[573,1928,719],{"className":1929},[784],[573,1931],{"className":1932,"style":780},[633],[573,1934,1936,1939,1942,1945,1948],{"className":1935},[615],[573,1937],{"className":1938,"style":794},[619],[573,1940,653],{"className":1941},[624,625],[573,1943],{"className":1944,"style":801},[633],[573,1946,724],{"className":1947},[805],[573,1949],{"className":1950,"style":801},[633],[573,1952,1954,1957,1960,1963,1966],{"className":1953},[615],[573,1955],{"className":1956,"style":815},[619],[573,1958,594],{"className":1959},[624,625],[573,1961],{"className":1962,"style":801},[633],[573,1964,729],{"className":1965},[805],[573,1967],{"className":1968,"style":801},[633],[573,1970,1972,1975,1978,1981,1984],{"className":1971},[615],[573,1973],{"className":1974,"style":834},[619],[573,1976,658],{"className":1977},[624,625],[573,1979],{"className":1980,"style":801},[633],[573,1982,724],{"className":1983},[805],[573,1985],{"className":1986,"style":801},[633],[573,1988,1990,1993],{"className":1989},[615],[573,1991],{"className":1992,"style":887},[619],[573,1994,1816],{"className":1995},[624,625],", dass ",[573,1998,2000,2046],{"className":1999},[576],[573,2001,2003],{"className":2002},[580],[582,2004,2005],{"xmlns":584},[586,2006,2007,2043],{},[589,2008,2009,2011,2013,2015,2018,2020,2022,2025,2027,2036,2039,2041],{},[592,2010,653],{},[596,2012,724],{},[592,2014,594],{},[596,2016,2017],{},"≡",[958,2019,960],{},[633,2021],{},[633,2023],{"width":2024},"0.4444em",[596,2026,707],{"stretchy":706},[589,2028,2029,2031,2034],{},[592,2030,1816],{"mathvariant":699},[592,2032,2033],{"mathvariant":699},"o",[592,2035,1332],{"mathvariant":699},[633,2037],{"width":2038},"0.3333em",[592,2040,1816],{},[596,2042,716],{"stretchy":706},[604,2044,2045],{"encoding":606},"s \\cdot a \\equiv 1 \\pmod m",[573,2047,2049,2067,2086,2103],{"className":2048,"ariaHidden":598},[611],[573,2050,2052,2055,2058,2061,2064],{"className":2051},[615],[573,2053],{"className":2054,"style":794},[619],[573,2056,653],{"className":2057},[624,625],[573,2059],{"className":2060,"style":801},[633],[573,2062,724],{"className":2063},[805],[573,2065],{"className":2066,"style":801},[633],[573,2068,2070,2074,2077,2080,2083],{"className":2069},[615],[573,2071],{"className":2072,"style":2073},[619],"height:0.4637em;",[573,2075,594],{"className":2076},[624,625],[573,2078],{"className":2079,"style":780},[633],[573,2081,2017],{"className":2082},[784],[573,2084],{"className":2085,"style":780},[633],[573,2087,2089,2092,2095,2099],{"className":2088},[615],[573,2090],{"className":2091,"style":1874},[619],[573,2093,960],{"className":2094},[624],[573,2096],{"className":2097},[633,2098],"allowbreak",[573,2100],{"className":2101,"style":2102},[633],"margin-right:0.4444em;",[573,2104,2106,2109,2112,2122,2126,2129],{"className":2105},[615],[573,2107],{"className":2108,"style":748},[619],[573,2110,707],{"className":2111},[760],[573,2113,2115],{"className":2114},[624],[573,2116,2118],{"className":2117},[624],[573,2119,2121],{"className":2120},[624,756],"mod",[573,2123],{"className":2124,"style":2125},[633],"margin-right:0.3333em;",[573,2127,1816],{"className":2128},[624,625],[573,2130,716],{"className":2131},[776],". Also ist ",[573,2134,2136,2149],{"className":2135},[576],[573,2137,2139],{"className":2138},[580],[582,2140,2141],{"xmlns":584},[586,2142,2143,2147],{},[589,2144,2145],{},[592,2146,653],{},[604,2148,653],{"encoding":606},[573,2150,2152],{"className":2151,"ariaHidden":598},[611],[573,2153,2155,2158],{"className":2154},[615],[573,2156],{"className":2157,"style":887},[619],[573,2159,653],{"className":2160},[624,625]," (auf ",[573,2163,2165,2193],{"className":2164},[576],[573,2166,2168],{"className":2167},[580],[582,2169,2170],{"xmlns":584},[586,2171,2172,2190],{},[589,2173,2174,2177,2179,2182,2184,2186,2188],{},[958,2175,2176],{},"0",[596,2178,599],{"separator":598},[596,2180,2181],{},"…",[596,2183,599],{"separator":598},[592,2185,1816],{},[596,2187,956],{},[958,2189,960],{},[604,2191,2192],{"encoding":606},"0, \\ldots, m-1",[573,2194,2196,2236],{"className":2195,"ariaHidden":598},[611],[573,2197,2199,2203,2206,2209,2212,2215,2218,2221,2224,2227,2230,2233],{"className":2198},[615],[573,2200],{"className":2201,"style":2202},[619],"height:0.8389em;vertical-align:-0.1944em;",[573,2204,2176],{"className":2205},[624],[573,2207,599],{"className":2208},[629],[573,2210],{"className":2211,"style":634},[633],[573,2213,2181],{"className":2214},[1483],[573,2216],{"className":2217,"style":634},[633],[573,2219,599],{"className":2220},[629],[573,2222],{"className":2223,"style":634},[633],[573,2225,1816],{"className":2226},[624,625],[573,2228],{"className":2229,"style":801},[633],[573,2231,956],{"className":2232},[805],[573,2234],{"className":2235,"style":801},[633],[573,2237,2239,2242],{"className":2238},[615],[573,2240],{"className":2241,"style":1874},[619],[573,2243,960],{"className":2244},[624]," reduziert) das Inverse von ",[573,2247,2249,2262],{"className":2248},[576],[573,2250,2252],{"className":2251},[580],[582,2253,2254],{"xmlns":584},[586,2255,2256,2260],{},[589,2257,2258],{},[592,2259,594],{},[604,2261,594],{"encoding":606},[573,2263,2265],{"className":2264,"ariaHidden":598},[611],[573,2266,2268,2271],{"className":2267},[615],[573,2269],{"className":2270,"style":887},[619],[573,2272,594],{"className":2273},[624,625]," modulo ",[573,2276,2278,2291],{"className":2277},[576],[573,2279,2281],{"className":2280},[580],[582,2282,2283],{"xmlns":584},[586,2284,2285,2289],{},[589,2286,2287],{},[592,2288,1816],{},[604,2290,1816],{"encoding":606},[573,2292,2294],{"className":2293,"ariaHidden":598},[611],[573,2295,2297,2300],{"className":2296},[615],[573,2298],{"className":2299,"style":887},[619],[573,2301,1816],{"className":2302},[624,625],". Das braucht man beim Chinesischen Restsatz und bei RSA.",[560,2305,2307],{"id":2306},"beispiele","Beispiele",[565,2309,2310,2374],{},[573,2311,2313,2341],{"className":2312},[576],[573,2314,2316],{"className":2315},[580],[582,2317,2318],{"xmlns":584},[586,2319,2320,2338],{},[589,2321,2322,2324,2326,2328,2331,2333,2336],{},[592,2323,700],{"mathvariant":699},[596,2325,703],{},[596,2327,707],{"stretchy":706},[958,2329,2330],{},"240",[596,2332,599],{"separator":598},[958,2334,2335],{},"46",[596,2337,716],{"stretchy":706},[604,2339,2340],{"encoding":606},"\\operatorname{ggT}(240, 46)",[573,2342,2344],{"className":2343,"ariaHidden":598},[611],[573,2345,2347,2350,2356,2359,2362,2365,2368,2371],{"className":2346},[615],[573,2348],{"className":2349,"style":748},[619],[573,2351,2353],{"className":2352},[752],[573,2354,700],{"className":2355},[624,756],[573,2357,707],{"className":2358},[760],[573,2360,2330],{"className":2361},[624],[573,2363,599],{"className":2364},[629],[573,2366],{"className":2367,"style":634},[633],[573,2369,2335],{"className":2370},[624],[573,2372,716],{"className":2373},[776]," als Kombination. Divisionen:",[573,2376,2379],{"className":2377},[2378],"katex-display",[573,2380,2382,2547],{"className":2381},[576],[573,2383,2385],{"className":2384},[580],[582,2386,2388],{"xmlns":584,"display":2387},"block",[586,2389,2390,2544],{},[2391,2392,2396,2429,2459,2487,2516],"mtable",{"rowspacing":2393,"columnalign":2394,"columnspacing":2395},"0.25em","right left","0em",[2397,2398,2399,2407],"mtr",{},[2400,2401,2402],"mtd",{},[2403,2404,2405],"mstyle",{"scriptlevel":2176,"displaystyle":598},[958,2406,2330],{},[2400,2408,2409],{},[2403,2410,2411],{"scriptlevel":2176,"displaystyle":598},[589,2412,2413,2415,2417,2420,2422,2424,2426],{},[589,2414],{},[596,2416,719],{},[958,2418,2419],{},"5",[596,2421,724],{},[958,2423,2335],{},[596,2425,729],{},[958,2427,2428],{},"10",[2397,2430,2431,2437],{},[2400,2432,2433],{},[2403,2434,2435],{"scriptlevel":2176,"displaystyle":598},[958,2436,2335],{},[2400,2438,2439],{},[2403,2440,2441],{"scriptlevel":2176,"displaystyle":598},[589,2442,2443,2445,2447,2450,2452,2454,2456],{},[589,2444],{},[596,2446,719],{},[958,2448,2449],{},"4",[596,2451,724],{},[958,2453,2428],{},[596,2455,729],{},[958,2457,2458],{},"6",[2397,2460,2461,2467],{},[2400,2462,2463],{},[2403,2464,2465],{"scriptlevel":2176,"displaystyle":598},[958,2466,2428],{},[2400,2468,2469],{},[2403,2470,2471],{"scriptlevel":2176,"displaystyle":598},[589,2472,2473,2475,2477,2479,2481,2483,2485],{},[589,2474],{},[596,2476,719],{},[958,2478,960],{},[596,2480,724],{},[958,2482,2458],{},[596,2484,729],{},[958,2486,2449],{},[2397,2488,2489,2495],{},[2400,2490,2491],{},[2403,2492,2493],{"scriptlevel":2176,"displaystyle":598},[958,2494,2458],{},[2400,2496,2497],{},[2403,2498,2499],{"scriptlevel":2176,"displaystyle":598},[589,2500,2501,2503,2505,2507,2509,2511,2513],{},[589,2502],{},[596,2504,719],{},[958,2506,960],{},[596,2508,724],{},[958,2510,2449],{},[596,2512,729],{},[958,2514,2515],{},"2",[2397,2517,2518,2524],{},[2400,2519,2520],{},[2403,2521,2522],{"scriptlevel":2176,"displaystyle":598},[958,2523,2449],{},[2400,2525,2526],{},[2403,2527,2528],{"scriptlevel":2176,"displaystyle":598},[589,2529,2530,2532,2534,2536,2538,2540,2542],{},[589,2531],{},[596,2533,719],{},[958,2535,2515],{},[596,2537,724],{},[958,2539,2515],{},[596,2541,729],{},[958,2543,2176],{},[604,2545,2546],{"encoding":606},"\\begin{aligned}\n240 &= 5 \\cdot 46 + 10 \\\\\n46 &= 4 \\cdot 10 + 6 \\\\\n10 &= 1 \\cdot 6 + 4 \\\\\n6 &= 1 \\cdot 4 + 2 \\\\\n4 &= 2 \\cdot 2 + 0\n\\end{aligned}",[573,2548,2550],{"className":2549,"ariaHidden":598},[611],[573,2551,2553,2557],{"className":2552},[615],[573,2554],{"className":2555,"style":2556},[619],"height:7.2em;vertical-align:-3.35em;",[573,2558,2560],{"className":2559},[624],[573,2561,2563,2649],{"className":2562},[2391],[573,2564,2567],{"className":2565},[2566],"col-align-r",[573,2568,2570,2640],{"className":2569},[1019,1020],[573,2571,2573,2637],{"className":2572},[1024],[573,2574,2577,2589,2601,2613,2625],{"className":2575,"style":2576},[1028],"height:3.85em;",[573,2578,2580,2583],{"style":2579},"top:-6.01em;",[573,2581],{"className":2582,"style":1544},[1036],[573,2584,2586],{"className":2585},[624],[573,2587,2330],{"className":2588},[624],[573,2590,2592,2595],{"style":2591},"top:-4.51em;",[573,2593],{"className":2594,"style":1544},[1036],[573,2596,2598],{"className":2597},[624],[573,2599,2335],{"className":2600},[624],[573,2602,2604,2607],{"style":2603},"top:-3.01em;",[573,2605],{"className":2606,"style":1544},[1036],[573,2608,2610],{"className":2609},[624],[573,2611,2428],{"className":2612},[624],[573,2614,2616,2619],{"style":2615},"top:-1.51em;",[573,2617],{"className":2618,"style":1544},[1036],[573,2620,2622],{"className":2621},[624],[573,2623,2458],{"className":2624},[624],[573,2626,2628,2631],{"style":2627},"top:-0.01em;",[573,2629],{"className":2630,"style":1544},[1036],[573,2632,2634],{"className":2633},[624],[573,2635,2449],{"className":2636},[624],[573,2638,1062],{"className":2639},[1061],[573,2641,2643],{"className":2642},[1024],[573,2644,2647],{"className":2645,"style":2646},[1028],"height:3.35em;",[573,2648],{},[573,2650,2653],{"className":2651},[2652],"col-align-l",[573,2654,2656,2900],{"className":2655},[1019,1020],[573,2657,2659,2897],{"className":2658},[1024],[573,2660,2662,2709,2756,2803,2850],{"className":2661,"style":2576},[1028],[573,2663,2664,2667],{"style":2579},[573,2665],{"className":2666,"style":1544},[1036],[573,2668,2670,2673,2676,2679,2682,2685,2688,2691,2694,2697,2700,2703,2706],{"className":2669},[624],[573,2671],{"className":2672},[624],[573,2674],{"className":2675,"style":780},[633],[573,2677,719],{"className":2678},[784],[573,2680],{"className":2681,"style":780},[633],[573,2683,2419],{"className":2684},[624],[573,2686],{"className":2687,"style":801},[633],[573,2689,724],{"className":2690},[805],[573,2692],{"className":2693,"style":801},[633],[573,2695,2335],{"className":2696},[624],[573,2698],{"className":2699,"style":801},[633],[573,2701,729],{"className":2702},[805],[573,2704],{"className":2705,"style":801},[633],[573,2707,2428],{"className":2708},[624],[573,2710,2711,2714],{"style":2591},[573,2712],{"className":2713,"style":1544},[1036],[573,2715,2717,2720,2723,2726,2729,2732,2735,2738,2741,2744,2747,2750,2753],{"className":2716},[624],[573,2718],{"className":2719},[624],[573,2721],{"className":2722,"style":780},[633],[573,2724,719],{"className":2725},[784],[573,2727],{"className":2728,"style":780},[633],[573,2730,2449],{"className":2731},[624],[573,2733],{"className":2734,"style":801},[633],[573,2736,724],{"className":2737},[805],[573,2739],{"className":2740,"style":801},[633],[573,2742,2428],{"className":2743},[624],[573,2745],{"className":2746,"style":801},[633],[573,2748,729],{"className":2749},[805],[573,2751],{"className":2752,"style":801},[633],[573,2754,2458],{"className":2755},[624],[573,2757,2758,2761],{"style":2603},[573,2759],{"className":2760,"style":1544},[1036],[573,2762,2764,2767,2770,2773,2776,2779,2782,2785,2788,2791,2794,2797,2800],{"className":2763},[624],[573,2765],{"className":2766},[624],[573,2768],{"className":2769,"style":780},[633],[573,2771,719],{"className":2772},[784],[573,2774],{"className":2775,"style":780},[633],[573,2777,960],{"className":2778},[624],[573,2780],{"className":2781,"style":801},[633],[573,2783,724],{"className":2784},[805],[573,2786],{"className":2787,"style":801},[633],[573,2789,2458],{"className":2790},[624],[573,2792],{"className":2793,"style":801},[633],[573,2795,729],{"className":2796},[805],[573,2798],{"className":2799,"style":801},[633],[573,2801,2449],{"className":2802},[624],[573,2804,2805,2808],{"style":2615},[573,2806],{"className":2807,"style":1544},[1036],[573,2809,2811,2814,2817,2820,2823,2826,2829,2832,2835,2838,2841,2844,2847],{"className":2810},[624],[573,2812],{"className":2813},[624],[573,2815],{"className":2816,"style":780},[633],[573,2818,719],{"className":2819},[784],[573,2821],{"className":2822,"style":780},[633],[573,2824,960],{"className":2825},[624],[573,2827],{"className":2828,"style":801},[633],[573,2830,724],{"className":2831},[805],[573,2833],{"className":2834,"style":801},[633],[573,2836,2449],{"className":2837},[624],[573,2839],{"className":2840,"style":801},[633],[573,2842,729],{"className":2843},[805],[573,2845],{"className":2846,"style":801},[633],[573,2848,2515],{"className":2849},[624],[573,2851,2852,2855],{"style":2627},[573,2853],{"className":2854,"style":1544},[1036],[573,2856,2858,2861,2864,2867,2870,2873,2876,2879,2882,2885,2888,2891,2894],{"className":2857},[624],[573,2859],{"className":2860},[624],[573,2862],{"className":2863,"style":780},[633],[573,2865,719],{"className":2866},[784],[573,2868],{"className":2869,"style":780},[633],[573,2871,2515],{"className":2872},[624],[573,2874],{"className":2875,"style":801},[633],[573,2877,724],{"className":2878},[805],[573,2880],{"className":2881,"style":801},[633],[573,2883,2515],{"className":2884},[624],[573,2886],{"className":2887,"style":801},[633],[573,2889,729],{"className":2890},[805],[573,2892],{"className":2893,"style":801},[633],[573,2895,2176],{"className":2896},[624],[573,2898,1062],{"className":2899},[1061],[573,2901,2903],{"className":2902},[1024],[573,2904,2906],{"className":2905,"style":2646},[1028],[573,2907],{},[565,2909,2910,2911,2995],{},"Also ",[573,2912,2914,2944],{"className":2913},[576],[573,2915,2917],{"className":2916},[580],[582,2918,2919],{"xmlns":584},[586,2920,2921,2941],{},[589,2922,2923,2925,2927,2929,2931,2933,2935,2937,2939],{},[592,2924,700],{"mathvariant":699},[596,2926,703],{},[596,2928,707],{"stretchy":706},[958,2930,2330],{},[596,2932,599],{"separator":598},[958,2934,2335],{},[596,2936,716],{"stretchy":706},[596,2938,719],{},[958,2940,2515],{},[604,2942,2943],{"encoding":606},"\\operatorname{ggT}(240, 46) = 2",[573,2945,2947,2986],{"className":2946,"ariaHidden":598},[611],[573,2948,2950,2953,2959,2962,2965,2968,2971,2974,2977,2980,2983],{"className":2949},[615],[573,2951],{"className":2952,"style":748},[619],[573,2954,2956],{"className":2955},[752],[573,2957,700],{"className":2958},[624,756],[573,2960,707],{"className":2961},[760],[573,2963,2330],{"className":2964},[624],[573,2966,599],{"className":2967},[629],[573,2969],{"className":2970,"style":634},[633],[573,2972,2335],{"className":2973},[624],[573,2975,716],{"className":2976},[776],[573,2978],{"className":2979,"style":780},[633],[573,2981,719],{"className":2982},[784],[573,2984],{"className":2985,"style":780},[633],[573,2987,2989,2992],{"className":2988},[615],[573,2990],{"className":2991,"style":1874},[619],[573,2993,2515],{"className":2994},[624],". Rückwärts einsetzen:",[573,2997,2999],{"className":2998},[2378],[573,3000,3002,3186],{"className":3001},[576],[573,3003,3005],{"className":3004},[580],[582,3006,3007],{"xmlns":584,"display":2387},[586,3008,3009,3183],{},[2391,3010,3011,3063,3120],{"rowspacing":2393,"columnalign":2394,"columnspacing":2395},[2397,3012,3013,3019],{},[2400,3014,3015],{},[2403,3016,3017],{"scriptlevel":2176,"displaystyle":598},[958,3018,2515],{},[2400,3020,3021],{},[2403,3022,3023],{"scriptlevel":2176,"displaystyle":598},[589,3024,3025,3027,3029,3031,3033,3035,3037,3039,3041,3043,3045,3047,3049,3051,3053,3055,3057,3059,3061],{},[589,3026],{},[596,3028,719],{},[958,3030,2458],{},[596,3032,956],{},[958,3034,2449],{},[596,3036,719],{},[958,3038,2458],{},[596,3040,956],{},[596,3042,707],{"stretchy":706},[958,3044,2428],{},[596,3046,956],{},[958,3048,2458],{},[596,3050,716],{"stretchy":706},[596,3052,719],{},[958,3054,2515],{},[596,3056,724],{},[958,3058,2458],{},[596,3060,956],{},[958,3062,2428],{},[2397,3064,3065,3071],{},[2400,3066,3067],{},[2403,3068,3069],{"scriptlevel":2176,"displaystyle":598},[589,3070],{},[2400,3072,3073],{},[2403,3074,3075],{"scriptlevel":2176,"displaystyle":598},[589,3076,3077,3079,3081,3083,3085,3087,3089,3091,3093,3095,3097,3099,3101,3103,3105,3107,3109,3111,3113,3116,3118],{},[589,3078],{},[596,3080,719],{},[958,3082,2515],{},[596,3084,724],{},[596,3086,707],{"stretchy":706},[958,3088,2335],{},[596,3090,956],{},[958,3092,2449],{},[596,3094,724],{},[958,3096,2428],{},[596,3098,716],{"stretchy":706},[596,3100,956],{},[958,3102,2428],{},[596,3104,719],{},[958,3106,2515],{},[596,3108,724],{},[958,3110,2335],{},[596,3112,956],{},[958,3114,3115],{},"9",[596,3117,724],{},[958,3119,2428],{},[2397,3121,3122,3128],{},[2400,3123,3124],{},[2403,3125,3126],{"scriptlevel":2176,"displaystyle":598},[589,3127],{},[2400,3129,3130],{},[2403,3131,3132],{"scriptlevel":2176,"displaystyle":598},[589,3133,3134,3136,3138,3140,3142,3144,3146,3148,3150,3152,3154,3156,3158,3160,3162,3164,3166,3168,3170,3172,3174,3176,3179,3181],{},[589,3135],{},[596,3137,719],{},[958,3139,2515],{},[596,3141,724],{},[958,3143,2335],{},[596,3145,956],{},[958,3147,3115],{},[596,3149,724],{},[596,3151,707],{"stretchy":706},[958,3153,2330],{},[596,3155,956],{},[958,3157,2419],{},[596,3159,724],{},[958,3161,2335],{},[596,3163,716],{"stretchy":706},[596,3165,719],{},[596,3167,956],{},[958,3169,3115],{},[596,3171,724],{},[958,3173,2330],{},[596,3175,729],{},[958,3177,3178],{},"47",[596,3180,724],{},[958,3182,2335],{},[604,3184,3185],{"encoding":606},"\\begin{aligned}\n2 &= 6 - 4 = 6 - (10 - 6) = 2 \\cdot 6 - 10 \\\\\n  &= 2 \\cdot (46 - 4 \\cdot 10) - 10 = 2 \\cdot 46 - 9 \\cdot 10 \\\\\n  &= 2 \\cdot 46 - 9 \\cdot (240 - 5 \\cdot 46) = -9 \\cdot 240 + 47 \\cdot 46\n\\end{aligned}",[573,3187,3189],{"className":3188,"ariaHidden":598},[611],[573,3190,3192,3196],{"className":3191},[615],[573,3193],{"className":3194,"style":3195},[619],"height:4.2em;vertical-align:-1.85em;",[573,3197,3199],{"className":3198},[624],[573,3200,3202,3254],{"className":3201},[2391],[573,3203,3205],{"className":3204},[2566],[573,3206,3208,3245],{"className":3207},[1019,1020],[573,3209,3211,3242],{"className":3210},[1024],[573,3212,3215,3226,3234],{"className":3213,"style":3214},[1028],"height:2.35em;",[573,3216,3217,3220],{"style":2591},[573,3218],{"className":3219,"style":1544},[1036],[573,3221,3223],{"className":3222},[624],[573,3224,2515],{"className":3225},[624],[573,3227,3228,3231],{"style":2603},[573,3229],{"className":3230,"style":1544},[1036],[573,3232],{"className":3233},[624],[573,3235,3236,3239],{"style":2615},[573,3237],{"className":3238,"style":1544},[1036],[573,3240],{"className":3241},[624],[573,3243,1062],{"className":3244},[1061],[573,3246,3248],{"className":3247},[1024],[573,3249,3252],{"className":3250,"style":3251},[1028],"height:1.85em;",[573,3253],{},[573,3255,3257],{"className":3256},[2652],[573,3258,3260,3647],{"className":3259},[1019,1020],[573,3261,3263,3644],{"className":3262},[1024],[573,3264,3266,3379,3504],{"className":3265,"style":3214},[1028],[573,3267,3268,3271],{"style":2591},[573,3269],{"className":3270,"style":1544},[1036],[573,3272,3274,3277,3280,3283,3286,3289,3292,3295,3298,3301,3304,3307,3310,3313,3316,3319,3322,3325,3328,3331,3334,3337,3340,3343,3346,3349,3352,3355,3358,3361,3364,3367,3370,3373,3376],{"className":3273},[624],[573,3275],{"className":3276},[624],[573,3278],{"className":3279,"style":780},[633],[573,3281,719],{"className":3282},[784],[573,3284],{"className":3285,"style":780},[633],[573,3287,2458],{"className":3288},[624],[573,3290],{"className":3291,"style":801},[633],[573,3293,956],{"className":3294},[805],[573,3296],{"className":3297,"style":801},[633],[573,3299,2449],{"className":3300},[624],[573,3302],{"className":3303,"style":780},[633],[573,3305,719],{"className":3306},[784],[573,3308],{"className":3309,"style":780},[633],[573,3311,2458],{"className":3312},[624],[573,3314],{"className":3315,"style":801},[633],[573,3317,956],{"className":3318},[805],[573,3320],{"className":3321,"style":801},[633],[573,3323,707],{"className":3324},[760],[573,3326,2428],{"className":3327},[624],[573,3329],{"className":3330,"style":801},[633],[573,3332,956],{"className":3333},[805],[573,3335],{"className":3336,"style":801},[633],[573,3338,2458],{"className":3339},[624],[573,3341,716],{"className":3342},[776],[573,3344],{"className":3345,"style":780},[633],[573,3347,719],{"className":3348},[784],[573,3350],{"className":3351,"style":780},[633],[573,3353,2515],{"className":3354},[624],[573,3356],{"className":3357,"style":801},[633],[573,3359,724],{"className":3360},[805],[573,3362],{"className":3363,"style":801},[633],[573,3365,2458],{"className":3366},[624],[573,3368],{"className":3369,"style":801},[633],[573,3371,956],{"className":3372},[805],[573,3374],{"className":3375,"style":801},[633],[573,3377,2428],{"className":3378},[624],[573,3380,3381,3384],{"style":2603},[573,3382],{"className":3383,"style":1544},[1036],[573,3385,3387,3390,3393,3396,3399,3402,3405,3408,3411,3414,3417,3420,3423,3426,3429,3432,3435,3438,3441,3444,3447,3450,3453,3456,3459,3462,3465,3468,3471,3474,3477,3480,3483,3486,3489,3492,3495,3498,3501],{"className":3386},[624],[573,3388],{"className":3389},[624],[573,3391],{"className":3392,"style":780},[633],[573,3394,719],{"className":3395},[784],[573,3397],{"className":3398,"style":780},[633],[573,3400,2515],{"className":3401},[624],[573,3403],{"className":3404,"style":801},[633],[573,3406,724],{"className":3407},[805],[573,3409],{"className":3410,"style":801},[633],[573,3412,707],{"className":3413},[760],[573,3415,2335],{"className":3416},[624],[573,3418],{"className":3419,"style":801},[633],[573,3421,956],{"className":3422},[805],[573,3424],{"className":3425,"style":801},[633],[573,3427,2449],{"className":3428},[624],[573,3430],{"className":3431,"style":801},[633],[573,3433,724],{"className":3434},[805],[573,3436],{"className":3437,"style":801},[633],[573,3439,2428],{"className":3440},[624],[573,3442,716],{"className":3443},[776],[573,3445],{"className":3446,"style":801},[633],[573,3448,956],{"className":3449},[805],[573,3451],{"className":3452,"style":801},[633],[573,3454,2428],{"className":3455},[624],[573,3457],{"className":3458,"style":780},[633],[573,3460,719],{"className":3461},[784],[573,3463],{"className":3464,"style":780},[633],[573,3466,2515],{"className":3467},[624],[573,3469],{"className":3470,"style":801},[633],[573,3472,724],{"className":3473},[805],[573,3475],{"className":3476,"style":801},[633],[573,3478,2335],{"className":3479},[624],[573,3481],{"className":3482,"style":801},[633],[573,3484,956],{"className":3485},[805],[573,3487],{"className":3488,"style":801},[633],[573,3490,3115],{"className":3491},[624],[573,3493],{"className":3494,"style":801},[633],[573,3496,724],{"className":3497},[805],[573,3499],{"className":3500,"style":801},[633],[573,3502,2428],{"className":3503},[624],[573,3505,3506,3509],{"style":2615},[573,3507],{"className":3508,"style":1544},[1036],[573,3510,3512,3515,3518,3521,3524,3527,3530,3533,3536,3539,3542,3545,3548,3551,3554,3557,3560,3563,3566,3569,3572,3575,3578,3581,3584,3587,3590,3593,3596,3599,3602,3605,3608,3611,3614,3617,3620,3623,3626,3629,3632,3635,3638,3641],{"className":3511},[624],[573,3513],{"className":3514},[624],[573,3516],{"className":3517,"style":780},[633],[573,3519,719],{"className":3520},[784],[573,3522],{"className":3523,"style":780},[633],[573,3525,2515],{"className":3526},[624],[573,3528],{"className":3529,"style":801},[633],[573,3531,724],{"className":3532},[805],[573,3534],{"className":3535,"style":801},[633],[573,3537,2335],{"className":3538},[624],[573,3540],{"className":3541,"style":801},[633],[573,3543,956],{"className":3544},[805],[573,3546],{"className":3547,"style":801},[633],[573,3549,3115],{"className":3550},[624],[573,3552],{"className":3553,"style":801},[633],[573,3555,724],{"className":3556},[805],[573,3558],{"className":3559,"style":801},[633],[573,3561,707],{"className":3562},[760],[573,3564,2330],{"className":3565},[624],[573,3567],{"className":3568,"style":801},[633],[573,3570,956],{"className":3571},[805],[573,3573],{"className":3574,"style":801},[633],[573,3576,2419],{"className":3577},[624],[573,3579],{"className":3580,"style":801},[633],[573,3582,724],{"className":3583},[805],[573,3585],{"className":3586,"style":801},[633],[573,3588,2335],{"className":3589},[624],[573,3591,716],{"className":3592},[776],[573,3594],{"className":3595,"style":780},[633],[573,3597,719],{"className":3598},[784],[573,3600],{"className":3601,"style":780},[633],[573,3603,956],{"className":3604},[624],[573,3606,3115],{"className":3607},[624],[573,3609],{"className":3610,"style":801},[633],[573,3612,724],{"className":3613},[805],[573,3615],{"className":3616,"style":801},[633],[573,3618,2330],{"className":3619},[624],[573,3621],{"className":3622,"style":801},[633],[573,3624,729],{"className":3625},[805],[573,3627],{"className":3628,"style":801},[633],[573,3630,3178],{"className":3631},[624],[573,3633],{"className":3634,"style":801},[633],[573,3636,724],{"className":3637},[805],[573,3639],{"className":3640,"style":801},[633],[573,3642,2335],{"className":3643},[624],[573,3645,1062],{"className":3646},[1061],[573,3648,3650],{"className":3649},[1024],[573,3651,3653],{"className":3652,"style":3251},[1028],[573,3654],{},[565,3656,3657,3658,3715,3716,3767,3768,3819,3820,1784],{},"Ergebnis: ",[573,3659,3661,3681],{"className":3660},[576],[573,3662,3664],{"className":3663},[580],[582,3665,3666],{"xmlns":584},[586,3667,3668,3678],{},[589,3669,3670,3672,3674,3676],{},[592,3671,653],{},[596,3673,719],{},[596,3675,956],{},[958,3677,3115],{},[604,3679,3680],{"encoding":606},"s = -9",[573,3682,3684,3702],{"className":3683,"ariaHidden":598},[611],[573,3685,3687,3690,3693,3696,3699],{"className":3686},[615],[573,3688],{"className":3689,"style":887},[619],[573,3691,653],{"className":3692},[624,625],[573,3694],{"className":3695,"style":780},[633],[573,3697,719],{"className":3698},[784],[573,3700],{"className":3701,"style":780},[633],[573,3703,3705,3709,3712],{"className":3704},[615],[573,3706],{"className":3707,"style":3708},[619],"height:0.7278em;vertical-align:-0.0833em;",[573,3710,956],{"className":3711},[624],[573,3713,3115],{"className":3714},[624],", ",[573,3717,3719,3737],{"className":3718},[576],[573,3720,3722],{"className":3721},[580],[582,3723,3724],{"xmlns":584},[586,3725,3726,3734],{},[589,3727,3728,3730,3732],{},[592,3729,658],{},[596,3731,719],{},[958,3733,3178],{},[604,3735,3736],{"encoding":606},"t = 47",[573,3738,3740,3758],{"className":3739,"ariaHidden":598},[611],[573,3741,3743,3746,3749,3752,3755],{"className":3742},[615],[573,3744],{"className":3745,"style":834},[619],[573,3747,658],{"className":3748},[624,625],[573,3750],{"className":3751,"style":780},[633],[573,3753,719],{"className":3754},[784],[573,3756],{"className":3757,"style":780},[633],[573,3759,3761,3764],{"className":3760},[615],[573,3762],{"className":3763,"style":1874},[619],[573,3765,3178],{"className":3766},[624],". Mit ",[573,3769,3771,3789],{"className":3770},[576],[573,3772,3774],{"className":3773},[580],[582,3775,3776],{"xmlns":584},[586,3777,3778,3786],{},[589,3779,3780,3782,3784],{},[592,3781,953],{},[596,3783,719],{},[958,3785,960],{},[604,3787,3788],{"encoding":606},"k = 1",[573,3790,3792,3810],{"className":3791,"ariaHidden":598},[611],[573,3793,3795,3798,3801,3804,3807],{"className":3794},[615],[573,3796],{"className":3797,"style":853},[619],[573,3799,953],{"className":3800,"style":1051},[624,625],[573,3802],{"className":3803,"style":780},[633],[573,3805,719],{"className":3806},[784],[573,3808],{"className":3809,"style":780},[633],[573,3811,3813,3816],{"className":3812},[615],[573,3814],{"className":3815,"style":1874},[619],[573,3817,960],{"className":3818},[624]," erhält man eine weitere Lösung: ",[573,3821,3823,3855],{"className":3822},[576],[573,3824,3826],{"className":3825},[580],[582,3827,3828],{"xmlns":584},[586,3829,3830,3852],{},[589,3831,3832,3835,3837,3839,3841,3844,3846,3848,3850],{},[958,3833,3834],{},"14",[596,3836,724],{},[958,3838,2330],{},[596,3840,956],{},[958,3842,3843],{},"73",[596,3845,724],{},[958,3847,2335],{},[596,3849,719],{},[958,3851,2515],{},[604,3853,3854],{"encoding":606},"14 \\cdot 240 - 73 \\cdot 46 = 2",[573,3856,3858,3876,3894,3912,3930],{"className":3857,"ariaHidden":598},[611],[573,3859,3861,3864,3867,3870,3873],{"className":3860},[615],[573,3862],{"className":3863,"style":1874},[619],[573,3865,3834],{"className":3866},[624],[573,3868],{"className":3869,"style":801},[633],[573,3871,724],{"className":3872},[805],[573,3874],{"className":3875,"style":801},[633],[573,3877,3879,3882,3885,3888,3891],{"className":3878},[615],[573,3880],{"className":3881,"style":3708},[619],[573,3883,2330],{"className":3884},[624],[573,3886],{"className":3887,"style":801},[633],[573,3889,956],{"className":3890},[805],[573,3892],{"className":3893,"style":801},[633],[573,3895,3897,3900,3903,3906,3909],{"className":3896},[615],[573,3898],{"className":3899,"style":1874},[619],[573,3901,3843],{"className":3902},[624],[573,3904],{"className":3905,"style":801},[633],[573,3907,724],{"className":3908},[805],[573,3910],{"className":3911,"style":801},[633],[573,3913,3915,3918,3921,3924,3927],{"className":3914},[615],[573,3916],{"className":3917,"style":1874},[619],[573,3919,2335],{"className":3920},[624],[573,3922],{"className":3923,"style":780},[633],[573,3925,719],{"className":3926},[784],[573,3928],{"className":3929,"style":780},[633],[573,3931,3933,3936],{"className":3932},[615],[573,3934],{"className":3935,"style":1874},[619],[573,3937,2515],{"className":3938},[624],[565,3940,3941,4003,4004,3715,4100,3715,4195,4290],{},[569,3942,3943,3944,2274,3973,4002],{},"Inverses von ",[573,3945,3947,3961],{"className":3946},[576],[573,3948,3950],{"className":3949},[580],[582,3951,3952],{"xmlns":584},[586,3953,3954,3959],{},[589,3955,3956],{},[958,3957,3958],{},"7",[604,3960,3958],{"encoding":606},[573,3962,3964],{"className":3963,"ariaHidden":598},[611],[573,3965,3967,3970],{"className":3966},[615],[573,3968],{"className":3969,"style":1874},[619],[573,3971,3958],{"className":3972},[624],[573,3974,3976,3990],{"className":3975},[576],[573,3977,3979],{"className":3978},[580],[582,3980,3981],{"xmlns":584},[586,3982,3983,3988],{},[589,3984,3985],{},[958,3986,3987],{},"26",[604,3989,3987],{"encoding":606},[573,3991,3993],{"className":3992,"ariaHidden":598},[611],[573,3994,3996,3999],{"className":3995},[615],[573,3997],{"className":3998,"style":1874},[619],[573,4000,3987],{"className":4001},[624],":"," ",[573,4005,4007,4034],{"className":4006},[576],[573,4008,4010],{"className":4009},[580],[582,4011,4012],{"xmlns":584},[586,4013,4014,4031],{},[589,4015,4016,4018,4020,4023,4025,4027,4029],{},[958,4017,3987],{},[596,4019,719],{},[958,4021,4022],{},"3",[596,4024,724],{},[958,4026,3958],{},[596,4028,729],{},[958,4030,2419],{},[604,4032,4033],{"encoding":606},"26 = 3 \\cdot 7 + 5",[573,4035,4037,4055,4073,4091],{"className":4036,"ariaHidden":598},[611],[573,4038,4040,4043,4046,4049,4052],{"className":4039},[615],[573,4041],{"className":4042,"style":1874},[619],[573,4044,3987],{"className":4045},[624],[573,4047],{"className":4048,"style":780},[633],[573,4050,719],{"className":4051},[784],[573,4053],{"className":4054,"style":780},[633],[573,4056,4058,4061,4064,4067,4070],{"className":4057},[615],[573,4059],{"className":4060,"style":1874},[619],[573,4062,4022],{"className":4063},[624],[573,4065],{"className":4066,"style":801},[633],[573,4068,724],{"className":4069},[805],[573,4071],{"className":4072,"style":801},[633],[573,4074,4076,4079,4082,4085,4088],{"className":4075},[615],[573,4077],{"className":4078,"style":3708},[619],[573,4080,3958],{"className":4081},[624],[573,4083],{"className":4084,"style":801},[633],[573,4086,729],{"className":4087},[805],[573,4089],{"className":4090,"style":801},[633],[573,4092,4094,4097],{"className":4093},[615],[573,4095],{"className":4096,"style":1874},[619],[573,4098,2419],{"className":4099},[624],[573,4101,4103,4129],{"className":4102},[576],[573,4104,4106],{"className":4105},[580],[582,4107,4108],{"xmlns":584},[586,4109,4110,4126],{},[589,4111,4112,4114,4116,4118,4120,4122,4124],{},[958,4113,3958],{},[596,4115,719],{},[958,4117,960],{},[596,4119,724],{},[958,4121,2419],{},[596,4123,729],{},[958,4125,2515],{},[604,4127,4128],{"encoding":606},"7 = 1 \\cdot 5 + 2",[573,4130,4132,4150,4168,4186],{"className":4131,"ariaHidden":598},[611],[573,4133,4135,4138,4141,4144,4147],{"className":4134},[615],[573,4136],{"className":4137,"style":1874},[619],[573,4139,3958],{"className":4140},[624],[573,4142],{"className":4143,"style":780},[633],[573,4145,719],{"className":4146},[784],[573,4148],{"className":4149,"style":780},[633],[573,4151,4153,4156,4159,4162,4165],{"className":4152},[615],[573,4154],{"className":4155,"style":1874},[619],[573,4157,960],{"className":4158},[624],[573,4160],{"className":4161,"style":801},[633],[573,4163,724],{"className":4164},[805],[573,4166],{"className":4167,"style":801},[633],[573,4169,4171,4174,4177,4180,4183],{"className":4170},[615],[573,4172],{"className":4173,"style":3708},[619],[573,4175,2419],{"className":4176},[624],[573,4178],{"className":4179,"style":801},[633],[573,4181,729],{"className":4182},[805],[573,4184],{"className":4185,"style":801},[633],[573,4187,4189,4192],{"className":4188},[615],[573,4190],{"className":4191,"style":1874},[619],[573,4193,2515],{"className":4194},[624],[573,4196,4198,4224],{"className":4197},[576],[573,4199,4201],{"className":4200},[580],[582,4202,4203],{"xmlns":584},[586,4204,4205,4221],{},[589,4206,4207,4209,4211,4213,4215,4217,4219],{},[958,4208,2419],{},[596,4210,719],{},[958,4212,2515],{},[596,4214,724],{},[958,4216,2515],{},[596,4218,729],{},[958,4220,960],{},[604,4222,4223],{"encoding":606},"5 = 2 \\cdot 2 + 1",[573,4225,4227,4245,4263,4281],{"className":4226,"ariaHidden":598},[611],[573,4228,4230,4233,4236,4239,4242],{"className":4229},[615],[573,4231],{"className":4232,"style":1874},[619],[573,4234,2419],{"className":4235},[624],[573,4237],{"className":4238,"style":780},[633],[573,4240,719],{"className":4241},[784],[573,4243],{"className":4244,"style":780},[633],[573,4246,4248,4251,4254,4257,4260],{"className":4247},[615],[573,4249],{"className":4250,"style":1874},[619],[573,4252,2515],{"className":4253},[624],[573,4255],{"className":4256,"style":801},[633],[573,4258,724],{"className":4259},[805],[573,4261],{"className":4262,"style":801},[633],[573,4264,4266,4269,4272,4275,4278],{"className":4265},[615],[573,4267],{"className":4268,"style":3708},[619],[573,4270,2515],{"className":4271},[624],[573,4273],{"className":4274,"style":801},[633],[573,4276,729],{"className":4277},[805],[573,4279],{"className":4280,"style":801},[633],[573,4282,4284,4287],{"className":4283},[615],[573,4285],{"className":4286,"style":1874},[619],[573,4288,960],{"className":4289},[624],". Rückwärts:",[573,4292,4294],{"className":4293},[2378],[573,4295,4297,4376],{"className":4296},[576],[573,4298,4300],{"className":4299},[580],[582,4301,4302],{"xmlns":584,"display":2387},[586,4303,4304,4373],{},[589,4305,4306,4308,4310,4312,4314,4316,4318,4320,4322,4324,4326,4328,4330,4332,4334,4336,4338,4340,4342,4344,4346,4348,4350,4352,4354,4356,4358,4360,4362,4364,4366,4369,4371],{},[958,4307,960],{},[596,4309,719],{},[958,4311,2419],{},[596,4313,956],{},[958,4315,2515],{},[596,4317,724],{},[958,4319,2515],{},[596,4321,719],{},[958,4323,2419],{},[596,4325,956],{},[958,4327,2515],{},[596,4329,724],{},[596,4331,707],{"stretchy":706},[958,4333,3958],{},[596,4335,956],{},[958,4337,2419],{},[596,4339,716],{"stretchy":706},[596,4341,719],{},[958,4343,4022],{},[596,4345,724],{},[958,4347,2419],{},[596,4349,956],{},[958,4351,2515],{},[596,4353,724],{},[958,4355,3958],{},[596,4357,719],{},[958,4359,4022],{},[596,4361,724],{},[958,4363,3987],{},[596,4365,956],{},[958,4367,4368],{},"11",[596,4370,724],{},[958,4372,3958],{},[604,4374,4375],{"encoding":606},"1 = 5 - 2 \\cdot 2 = 5 - 2 \\cdot (7 - 5) = 3 \\cdot 5 - 2 \\cdot 7 = 3 \\cdot 26 - 11 \\cdot 7",[573,4377,4379,4397,4415,4433,4451,4469,4487,4508,4529,4547,4565,4583,4601,4619,4637,4655],{"className":4378,"ariaHidden":598},[611],[573,4380,4382,4385,4388,4391,4394],{"className":4381},[615],[573,4383],{"className":4384,"style":1874},[619],[573,4386,960],{"className":4387},[624],[573,4389],{"className":4390,"style":780},[633],[573,4392,719],{"className":4393},[784],[573,4395],{"className":4396,"style":780},[633],[573,4398,4400,4403,4406,4409,4412],{"className":4399},[615],[573,4401],{"className":4402,"style":3708},[619],[573,4404,2419],{"className":4405},[624],[573,4407],{"className":4408,"style":801},[633],[573,4410,956],{"className":4411},[805],[573,4413],{"className":4414,"style":801},[633],[573,4416,4418,4421,4424,4427,4430],{"className":4417},[615],[573,4419],{"className":4420,"style":1874},[619],[573,4422,2515],{"className":4423},[624],[573,4425],{"className":4426,"style":801},[633],[573,4428,724],{"className":4429},[805],[573,4431],{"className":4432,"style":801},[633],[573,4434,4436,4439,4442,4445,4448],{"className":4435},[615],[573,4437],{"className":4438,"style":1874},[619],[573,4440,2515],{"className":4441},[624],[573,4443],{"className":4444,"style":780},[633],[573,4446,719],{"className":4447},[784],[573,4449],{"className":4450,"style":780},[633],[573,4452,4454,4457,4460,4463,4466],{"className":4453},[615],[573,4455],{"className":4456,"style":3708},[619],[573,4458,2419],{"className":4459},[624],[573,4461],{"className":4462,"style":801},[633],[573,4464,956],{"className":4465},[805],[573,4467],{"className":4468,"style":801},[633],[573,4470,4472,4475,4478,4481,4484],{"className":4471},[615],[573,4473],{"className":4474,"style":1874},[619],[573,4476,2515],{"className":4477},[624],[573,4479],{"className":4480,"style":801},[633],[573,4482,724],{"className":4483},[805],[573,4485],{"className":4486,"style":801},[633],[573,4488,4490,4493,4496,4499,4502,4505],{"className":4489},[615],[573,4491],{"className":4492,"style":748},[619],[573,4494,707],{"className":4495},[760],[573,4497,3958],{"className":4498},[624],[573,4500],{"className":4501,"style":801},[633],[573,4503,956],{"className":4504},[805],[573,4506],{"className":4507,"style":801},[633],[573,4509,4511,4514,4517,4520,4523,4526],{"className":4510},[615],[573,4512],{"className":4513,"style":748},[619],[573,4515,2419],{"className":4516},[624],[573,4518,716],{"className":4519},[776],[573,4521],{"className":4522,"style":780},[633],[573,4524,719],{"className":4525},[784],[573,4527],{"className":4528,"style":780},[633],[573,4530,4532,4535,4538,4541,4544],{"className":4531},[615],[573,4533],{"className":4534,"style":1874},[619],[573,4536,4022],{"className":4537},[624],[573,4539],{"className":4540,"style":801},[633],[573,4542,724],{"className":4543},[805],[573,4545],{"className":4546,"style":801},[633],[573,4548,4550,4553,4556,4559,4562],{"className":4549},[615],[573,4551],{"className":4552,"style":3708},[619],[573,4554,2419],{"className":4555},[624],[573,4557],{"className":4558,"style":801},[633],[573,4560,956],{"className":4561},[805],[573,4563],{"className":4564,"style":801},[633],[573,4566,4568,4571,4574,4577,4580],{"className":4567},[615],[573,4569],{"className":4570,"style":1874},[619],[573,4572,2515],{"className":4573},[624],[573,4575],{"className":4576,"style":801},[633],[573,4578,724],{"className":4579},[805],[573,4581],{"className":4582,"style":801},[633],[573,4584,4586,4589,4592,4595,4598],{"className":4585},[615],[573,4587],{"className":4588,"style":1874},[619],[573,4590,3958],{"className":4591},[624],[573,4593],{"className":4594,"style":780},[633],[573,4596,719],{"className":4597},[784],[573,4599],{"className":4600,"style":780},[633],[573,4602,4604,4607,4610,4613,4616],{"className":4603},[615],[573,4605],{"className":4606,"style":1874},[619],[573,4608,4022],{"className":4609},[624],[573,4611],{"className":4612,"style":801},[633],[573,4614,724],{"className":4615},[805],[573,4617],{"className":4618,"style":801},[633],[573,4620,4622,4625,4628,4631,4634],{"className":4621},[615],[573,4623],{"className":4624,"style":3708},[619],[573,4626,3987],{"className":4627},[624],[573,4629],{"className":4630,"style":801},[633],[573,4632,956],{"className":4633},[805],[573,4635],{"className":4636,"style":801},[633],[573,4638,4640,4643,4646,4649,4652],{"className":4639},[615],[573,4641],{"className":4642,"style":1874},[619],[573,4644,4368],{"className":4645},[624],[573,4647],{"className":4648,"style":801},[633],[573,4650,724],{"className":4651},[805],[573,4653],{"className":4654,"style":801},[633],[573,4656,4658,4661],{"className":4657},[615],[573,4659],{"className":4660,"style":1874},[619],[573,4662,3958],{"className":4663},[624],[565,4665,2910,4666,4797,4798,4877,4878,1784],{},[573,4667,4669,4713],{"className":4668},[576],[573,4670,4672],{"className":4671},[580],[582,4673,4674],{"xmlns":584},[586,4675,4676,4710],{},[589,4677,4678,4680,4682,4684,4686,4688,4690,4692,4694,4696,4704,4706,4708],{},[596,4679,956],{},[958,4681,4368],{},[596,4683,724],{},[958,4685,3958],{},[596,4687,2017],{},[958,4689,960],{},[633,4691],{},[633,4693],{"width":2024},[596,4695,707],{"stretchy":706},[589,4697,4698,4700,4702],{},[592,4699,1816],{"mathvariant":699},[592,4701,2033],{"mathvariant":699},[592,4703,1332],{"mathvariant":699},[633,4705],{"width":2038},[958,4707,3987],{},[596,4709,716],{"stretchy":706},[604,4711,4712],{"encoding":606},"-11 \\cdot 7 \\equiv 1 \\pmod{26}",[573,4714,4716,4737,4755,4770],{"className":4715,"ariaHidden":598},[611],[573,4717,4719,4722,4725,4728,4731,4734],{"className":4718},[615],[573,4720],{"className":4721,"style":3708},[619],[573,4723,956],{"className":4724},[624],[573,4726,4368],{"className":4727},[624],[573,4729],{"className":4730,"style":801},[633],[573,4732,724],{"className":4733},[805],[573,4735],{"className":4736,"style":801},[633],[573,4738,4740,4743,4746,4749,4752],{"className":4739},[615],[573,4741],{"className":4742,"style":1874},[619],[573,4744,3958],{"className":4745},[624],[573,4747],{"className":4748,"style":780},[633],[573,4750,2017],{"className":4751},[784],[573,4753],{"className":4754,"style":780},[633],[573,4756,4758,4761,4764,4767],{"className":4757},[615],[573,4759],{"className":4760,"style":1874},[619],[573,4762,960],{"className":4763},[624],[573,4765],{"className":4766},[633,2098],[573,4768],{"className":4769,"style":2102},[633],[573,4771,4773,4776,4779,4788,4791,4794],{"className":4772},[615],[573,4774],{"className":4775,"style":748},[619],[573,4777,707],{"className":4778},[760],[573,4780,4782],{"className":4781},[624],[573,4783,4785],{"className":4784},[624],[573,4786,2121],{"className":4787},[624,756],[573,4789],{"className":4790,"style":2125},[633],[573,4792,3987],{"className":4793},[624],[573,4795,716],{"className":4796},[776],". Das Inverse ist ",[573,4799,4801,4826],{"className":4800},[576],[573,4802,4804],{"className":4803},[580],[582,4805,4806],{"xmlns":584},[586,4807,4808,4823],{},[589,4809,4810,4812,4814,4816,4818,4820],{},[596,4811,956],{},[958,4813,4368],{},[596,4815,729],{},[958,4817,3987],{},[596,4819,719],{},[958,4821,4822],{},"15",[604,4824,4825],{"encoding":606},"-11 + 26 = 15",[573,4827,4829,4850,4868],{"className":4828,"ariaHidden":598},[611],[573,4830,4832,4835,4838,4841,4844,4847],{"className":4831},[615],[573,4833],{"className":4834,"style":3708},[619],[573,4836,956],{"className":4837},[624],[573,4839,4368],{"className":4840},[624],[573,4842],{"className":4843,"style":801},[633],[573,4845,729],{"className":4846},[805],[573,4848],{"className":4849,"style":801},[633],[573,4851,4853,4856,4859,4862,4865],{"className":4852},[615],[573,4854],{"className":4855,"style":1874},[619],[573,4857,3987],{"className":4858},[624],[573,4860],{"className":4861,"style":780},[633],[573,4863,719],{"className":4864},[784],[573,4866],{"className":4867,"style":780},[633],[573,4869,4871,4874],{"className":4870},[615],[573,4872],{"className":4873,"style":1874},[619],[573,4875,4822],{"className":4876},[624],". Probe: ",[573,4879,4881,4916],{"className":4880},[576],[573,4882,4884],{"className":4883},[580],[582,4885,4886],{"xmlns":584},[586,4887,4888,4913],{},[589,4889,4890,4892,4894,4896,4898,4901,4903,4905,4907,4909,4911],{},[958,4891,3958],{},[596,4893,724],{},[958,4895,4822],{},[596,4897,719],{},[958,4899,4900],{},"105",[596,4902,719],{},[958,4904,2449],{},[596,4906,724],{},[958,4908,3987],{},[596,4910,729],{},[958,4912,960],{},[604,4914,4915],{"encoding":606},"7 \\cdot 15 = 105 = 4 \\cdot 26 + 1",[573,4917,4919,4937,4955,4973,4991,5009],{"className":4918,"ariaHidden":598},[611],[573,4920,4922,4925,4928,4931,4934],{"className":4921},[615],[573,4923],{"className":4924,"style":1874},[619],[573,4926,3958],{"className":4927},[624],[573,4929],{"className":4930,"style":801},[633],[573,4932,724],{"className":4933},[805],[573,4935],{"className":4936,"style":801},[633],[573,4938,4940,4943,4946,4949,4952],{"className":4939},[615],[573,4941],{"className":4942,"style":1874},[619],[573,4944,4822],{"className":4945},[624],[573,4947],{"className":4948,"style":780},[633],[573,4950,719],{"className":4951},[784],[573,4953],{"className":4954,"style":780},[633],[573,4956,4958,4961,4964,4967,4970],{"className":4957},[615],[573,4959],{"className":4960,"style":1874},[619],[573,4962,4900],{"className":4963},[624],[573,4965],{"className":4966,"style":780},[633],[573,4968,719],{"className":4969},[784],[573,4971],{"className":4972,"style":780},[633],[573,4974,4976,4979,4982,4985,4988],{"className":4975},[615],[573,4977],{"className":4978,"style":1874},[619],[573,4980,2449],{"className":4981},[624],[573,4983],{"className":4984,"style":801},[633],[573,4986,724],{"className":4987},[805],[573,4989],{"className":4990,"style":801},[633],[573,4992,4994,4997,5000,5003,5006],{"className":4993},[615],[573,4995],{"className":4996,"style":3708},[619],[573,4998,3987],{"className":4999},[624],[573,5001],{"className":5002,"style":801},[633],[573,5004,729],{"className":5005},[805],[573,5007],{"className":5008,"style":801},[633],[573,5010,5012,5015],{"className":5011},[615],[573,5013],{"className":5014,"style":1874},[619],[573,5016,960],{"className":5017},[624],[560,5019,5021],{"id":5020},"typische-fehler","Typische Fehler",[5023,5024,5025,5243,5426,5715],"ul",{},[928,5026,5027,5030,5031,5146,5147,5242],{},[569,5028,5029],{},"Vorzeichenfehler beim Einsetzen."," Beim Ersetzen eines Rests muss die ganze Klammer mit dem Koeffizienten multipliziert werden: ",[573,5032,5034,5068],{"className":5033},[576],[573,5035,5037],{"className":5036},[580],[582,5038,5039],{"xmlns":584},[586,5040,5041,5065],{},[589,5042,5043,5045,5047,5049,5051,5053,5055,5057,5059,5061,5063],{},[596,5044,956],{},[596,5046,707],{"stretchy":706},[958,5048,2428],{},[596,5050,956],{},[958,5052,2458],{},[596,5054,716],{"stretchy":706},[596,5056,719],{},[596,5058,956],{},[958,5060,2428],{},[596,5062,729],{},[958,5064,2458],{},[604,5066,5067],{"encoding":606},"-(10 - 6) = -10 + 6",[573,5069,5071,5095,5116,5137],{"className":5070,"ariaHidden":598},[611],[573,5072,5074,5077,5080,5083,5086,5089,5092],{"className":5073},[615],[573,5075],{"className":5076,"style":748},[619],[573,5078,956],{"className":5079},[624],[573,5081,707],{"className":5082},[760],[573,5084,2428],{"className":5085},[624],[573,5087],{"className":5088,"style":801},[633],[573,5090,956],{"className":5091},[805],[573,5093],{"className":5094,"style":801},[633],[573,5096,5098,5101,5104,5107,5110,5113],{"className":5097},[615],[573,5099],{"className":5100,"style":748},[619],[573,5102,2458],{"className":5103},[624],[573,5105,716],{"className":5106},[776],[573,5108],{"className":5109,"style":780},[633],[573,5111,719],{"className":5112},[784],[573,5114],{"className":5115,"style":780},[633],[573,5117,5119,5122,5125,5128,5131,5134],{"className":5118},[615],[573,5120],{"className":5121,"style":3708},[619],[573,5123,956],{"className":5124},[624],[573,5126,2428],{"className":5127},[624],[573,5129],{"className":5130,"style":801},[633],[573,5132,729],{"className":5133},[805],[573,5135],{"className":5136,"style":801},[633],[573,5138,5140,5143],{"className":5139},[615],[573,5141],{"className":5142,"style":1874},[619],[573,5144,2458],{"className":5145},[624],". Am Ende immer die Probe ",[573,5148,5150,5176],{"className":5149},[576],[573,5151,5153],{"className":5152},[580],[582,5154,5155],{"xmlns":584},[586,5156,5157,5173],{},[589,5158,5159,5161,5163,5165,5167,5169,5171],{},[592,5160,653],{},[596,5162,724],{},[592,5164,594],{},[596,5166,729],{},[592,5168,658],{},[596,5170,724],{},[592,5172,602],{},[604,5174,5175],{"encoding":606},"s \\cdot a + t \\cdot b",[573,5177,5179,5197,5215,5233],{"className":5178,"ariaHidden":598},[611],[573,5180,5182,5185,5188,5191,5194],{"className":5181},[615],[573,5183],{"className":5184,"style":794},[619],[573,5186,653],{"className":5187},[624,625],[573,5189],{"className":5190,"style":801},[633],[573,5192,724],{"className":5193},[805],[573,5195],{"className":5196,"style":801},[633],[573,5198,5200,5203,5206,5209,5212],{"className":5199},[615],[573,5201],{"className":5202,"style":815},[619],[573,5204,594],{"className":5205},[624,625],[573,5207],{"className":5208,"style":801},[633],[573,5210,729],{"className":5211},[805],[573,5213],{"className":5214,"style":801},[633],[573,5216,5218,5221,5224,5227,5230],{"className":5217},[615],[573,5219],{"className":5220,"style":834},[619],[573,5222,658],{"className":5223},[624,625],[573,5225],{"className":5226,"style":801},[633],[573,5228,724],{"className":5229},[805],[573,5231],{"className":5232,"style":801},[633],[573,5234,5236,5239],{"className":5235},[615],[573,5237],{"className":5238,"style":853},[619],[573,5240,602],{"className":5241},[624,625]," rechnen.",[928,5244,5245,4003,5248,5282,5283,2274,5311,5339,5340,5368,5369,891,5397,1784],{},[569,5246,5247],{},"Negatives Inverses stehen lassen.",[573,5249,5251,5267],{"className":5250},[576],[573,5252,5254],{"className":5253},[580],[582,5255,5256],{"xmlns":584},[586,5257,5258,5264],{},[589,5259,5260,5262],{},[596,5261,956],{},[958,5263,4368],{},[604,5265,5266],{"encoding":606},"-11",[573,5268,5270],{"className":5269,"ariaHidden":598},[611],[573,5271,5273,5276,5279],{"className":5272},[615],[573,5274],{"className":5275,"style":3708},[619],[573,5277,956],{"className":5278},[624],[573,5280,4368],{"className":5281},[624]," ist zwar ein Inverses von ",[573,5284,5286,5299],{"className":5285},[576],[573,5287,5289],{"className":5288},[580],[582,5290,5291],{"xmlns":584},[586,5292,5293,5297],{},[589,5294,5295],{},[958,5296,3958],{},[604,5298,3958],{"encoding":606},[573,5300,5302],{"className":5301,"ariaHidden":598},[611],[573,5303,5305,5308],{"className":5304},[615],[573,5306],{"className":5307,"style":1874},[619],[573,5309,3958],{"className":5310},[624],[573,5312,5314,5327],{"className":5313},[576],[573,5315,5317],{"className":5316},[580],[582,5318,5319],{"xmlns":584},[586,5320,5321,5325],{},[589,5322,5323],{},[958,5324,3987],{},[604,5326,3987],{"encoding":606},[573,5328,5330],{"className":5329,"ariaHidden":598},[611],[573,5331,5333,5336],{"className":5332},[615],[573,5334],{"className":5335,"style":1874},[619],[573,5337,3987],{"className":5338},[624],", üblich ist aber der Vertreter ",[573,5341,5343,5356],{"className":5342},[576],[573,5344,5346],{"className":5345},[580],[582,5347,5348],{"xmlns":584},[586,5349,5350,5354],{},[589,5351,5352],{},[958,5353,4822],{},[604,5355,4822],{"encoding":606},[573,5357,5359],{"className":5358,"ariaHidden":598},[611],[573,5360,5362,5365],{"className":5361},[615],[573,5363],{"className":5364,"style":1874},[619],[573,5366,4822],{"className":5367},[624]," zwischen ",[573,5370,5372,5385],{"className":5371},[576],[573,5373,5375],{"className":5374},[580],[582,5376,5377],{"xmlns":584},[586,5378,5379,5383],{},[589,5380,5381],{},[958,5382,2176],{},[604,5384,2176],{"encoding":606},[573,5386,5388],{"className":5387,"ariaHidden":598},[611],[573,5389,5391,5394],{"className":5390},[615],[573,5392],{"className":5393,"style":1874},[619],[573,5395,2176],{"className":5396},[624],[573,5398,5400,5414],{"className":5399},[576],[573,5401,5403],{"className":5402},[580],[582,5404,5405],{"xmlns":584},[586,5406,5407,5412],{},[589,5408,5409],{},[958,5410,5411],{},"25",[604,5413,5411],{"encoding":606},[573,5415,5417],{"className":5416,"ariaHidden":598},[611],[573,5418,5420,5423],{"className":5419},[615],[573,5421],{"className":5422,"style":1874},[619],[573,5424,5411],{"className":5425},[624],[928,5427,5428,5431,5432,5460,5461,5489,5490,5573,5574,5657,5658,2274,5686,5714],{},[569,5429,5430],{},"Ein Inverses suchen, wo keines existiert."," Modulo ",[573,5433,5435,5448],{"className":5434},[576],[573,5436,5438],{"className":5437},[580],[582,5439,5440],{"xmlns":584},[586,5441,5442,5446],{},[589,5443,5444],{},[592,5445,1816],{},[604,5447,1816],{"encoding":606},[573,5449,5451],{"className":5450,"ariaHidden":598},[611],[573,5452,5454,5457],{"className":5453},[615],[573,5455],{"className":5456,"style":887},[619],[573,5458,1816],{"className":5459},[624,625]," ist ",[573,5462,5464,5477],{"className":5463},[576],[573,5465,5467],{"className":5466},[580],[582,5468,5469],{"xmlns":584},[586,5470,5471,5475],{},[589,5472,5473],{},[592,5474,594],{},[604,5476,594],{"encoding":606},[573,5478,5480],{"className":5479,"ariaHidden":598},[611],[573,5481,5483,5486],{"className":5482},[615],[573,5484],{"className":5485,"style":887},[619],[573,5487,594],{"className":5488},[624,625]," nur invertierbar, wenn ",[573,5491,5493,5522],{"className":5492},[576],[573,5494,5496],{"className":5495},[580],[582,5497,5498],{"xmlns":584},[586,5499,5500,5520],{},[589,5501,5502,5504,5506,5508,5510,5512,5514,5516,5518],{},[592,5503,700],{"mathvariant":699},[596,5505,703],{},[596,5507,707],{"stretchy":706},[592,5509,594],{},[596,5511,599],{"separator":598},[592,5513,1816],{},[596,5515,716],{"stretchy":706},[596,5517,719],{},[958,5519,960],{},[604,5521,1825],{"encoding":606},[573,5523,5525,5564],{"className":5524,"ariaHidden":598},[611],[573,5526,5528,5531,5537,5540,5543,5546,5549,5552,5555,5558,5561],{"className":5527},[615],[573,5529],{"className":5530,"style":748},[619],[573,5532,5534],{"className":5533},[752],[573,5535,700],{"className":5536},[624,756],[573,5538,707],{"className":5539},[760],[573,5541,594],{"className":5542},[624,625],[573,5544,599],{"className":5545},[629],[573,5547],{"className":5548,"style":634},[633],[573,5550,1816],{"className":5551},[624,625],[573,5553,716],{"className":5554},[776],[573,5556],{"className":5557,"style":780},[633],[573,5559,719],{"className":5560},[784],[573,5562],{"className":5563,"style":780},[633],[573,5565,5567,5570],{"className":5566},[615],[573,5568],{"className":5569,"style":1874},[619],[573,5571,960],{"className":5572},[624],". Wegen ",[573,5575,5577,5606],{"className":5576},[576],[573,5578,5580],{"className":5579},[580],[582,5581,5582],{"xmlns":584},[586,5583,5584,5604],{},[589,5585,5586,5588,5590,5592,5594,5596,5598,5600,5602],{},[592,5587,700],{"mathvariant":699},[596,5589,703],{},[596,5591,707],{"stretchy":706},[958,5593,2330],{},[596,5595,599],{"separator":598},[958,5597,2335],{},[596,5599,716],{"stretchy":706},[596,5601,719],{},[958,5603,2515],{},[604,5605,2943],{"encoding":606},[573,5607,5609,5648],{"className":5608,"ariaHidden":598},[611],[573,5610,5612,5615,5621,5624,5627,5630,5633,5636,5639,5642,5645],{"className":5611},[615],[573,5613],{"className":5614,"style":748},[619],[573,5616,5618],{"className":5617},[752],[573,5619,700],{"className":5620},[624,756],[573,5622,707],{"className":5623},[760],[573,5625,2330],{"className":5626},[624],[573,5628,599],{"className":5629},[629],[573,5631],{"className":5632,"style":634},[633],[573,5634,2335],{"className":5635},[624],[573,5637,716],{"className":5638},[776],[573,5640],{"className":5641,"style":780},[633],[573,5643,719],{"className":5644},[784],[573,5646],{"className":5647,"style":780},[633],[573,5649,5651,5654],{"className":5650},[615],[573,5652],{"className":5653,"style":1874},[619],[573,5655,2515],{"className":5656},[624]," hat ",[573,5659,5661,5674],{"className":5660},[576],[573,5662,5664],{"className":5663},[580],[582,5665,5666],{"xmlns":584},[586,5667,5668,5672],{},[589,5669,5670],{},[958,5671,2335],{},[604,5673,2335],{"encoding":606},[573,5675,5677],{"className":5676,"ariaHidden":598},[611],[573,5678,5680,5683],{"className":5679},[615],[573,5681],{"className":5682,"style":1874},[619],[573,5684,2335],{"className":5685},[624],[573,5687,5689,5702],{"className":5688},[576],[573,5690,5692],{"className":5691},[580],[582,5693,5694],{"xmlns":584},[586,5695,5696,5700],{},[589,5697,5698],{},[958,5699,2330],{},[604,5701,2330],{"encoding":606},[573,5703,5705],{"className":5704,"ariaHidden":598},[611],[573,5706,5708,5711],{"className":5707},[615],[573,5709],{"className":5710,"style":1874},[619],[573,5712,2330],{"className":5713},[624]," kein Inverses.",[928,5716,5717,5776],{},[569,5718,5719,891,5747,5775],{},[573,5720,5722,5735],{"className":5721},[576],[573,5723,5725],{"className":5724},[580],[582,5726,5727],{"xmlns":584},[586,5728,5729,5733],{},[589,5730,5731],{},[592,5732,653],{},[604,5734,653],{"encoding":606},[573,5736,5738],{"className":5737,"ariaHidden":598},[611],[573,5739,5741,5744],{"className":5740},[615],[573,5742],{"className":5743,"style":887},[619],[573,5745,653],{"className":5746},[624,625],[573,5748,5750,5763],{"className":5749},[576],[573,5751,5753],{"className":5752},[580],[582,5754,5755],{"xmlns":584},[586,5756,5757,5761],{},[589,5758,5759],{},[592,5760,658],{},[604,5762,658],{"encoding":606},[573,5764,5766],{"className":5765,"ariaHidden":598},[611],[573,5767,5769,5772],{"className":5768},[615],[573,5770],{"className":5771,"style":834},[619],[573,5773,658],{"className":5774},[624,625]," für eindeutig halten."," Es gibt unendlich viele Paare; zwei verschiedene Ergebnisse können beide richtig sein.",{"title":5778,"searchDepth":5779,"depth":5779,"links":5780},"",2,[5781,5782,5783],{"id":562,"depth":5779,"text":563},{"id":2306,"depth":5779,"text":2307},{"id":5020,"depth":5779,"text":5021},[5785,5787,5789,5791,5793,5795,5797,5799,5801,5803,5805,5807,5809,5811,5813,5815],{"lhs":5786,"rhs":2330},"5*46 + 10",{"lhs":5788,"rhs":2335},"4*10 + 6",{"lhs":5790,"rhs":2428},"1*6 + 4",{"lhs":5792,"rhs":2458},"1*4 + 2",{"lhs":5794,"rhs":2449},"2*2",{"lhs":5796,"rhs":2515},"gcd(240, 46)",{"lhs":5798,"rhs":2515},"-9*240 + 47*46",{"lhs":5800,"rhs":2515},"2*46 - 9*10",{"lhs":5802,"rhs":2515},"14*240 - 73*46",{"lhs":5804,"rhs":3987},"3*7 + 5",{"lhs":5806,"rhs":3958},"1*5 + 2",{"lhs":5808,"rhs":2419},"2*2 + 1",{"lhs":5810,"rhs":960},"3*26 - 11*7",{"lhs":5812,"rhs":4822},"-11 + 26",{"lhs":5814,"rhs":960},"mod(7*15, 26)",{"lhs":5816,"rhs":5817},"7*15","4*26 + 1","a, b \\in \\mathbb{Z},\\ (a, b) \\neq (0, 0),\\ s, t \\in \\mathbb{Z}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">Z\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a, b \\in \\mathbb{Z},\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8833em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">Z\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>b\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">(a, b) \\neq (0, 0),\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan 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mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fdiscrete-math\u002Ferweiterter-euklidischer-algorithmus",[],[5830,5831,5832,5833],"euclidean-algorithm","modular-arithmetic","chinese-remainder","gcd-lcm",{"title":548,"description":5778},"de\u002Fformulas\u002Fmath\u002Fdiscrete-math\u002Ferweiterter-euklidischer-algorithmus","Der ggT zweier Zahlen lässt sich als ganzzahlige Kombination s·a + t·b schreiben; s und t liefert der erweiterte Algorithmus.",[5838,5839,5840,5841],"ggt","lemma von bézout","modulares inverses","zahlentheorie",[5843,5846,5850],{"symbol":607,"meaning":5844,"symbolHtml":5845},"ganze Zahlen, nicht beide null","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo 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style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">t\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","0fLR35hfAVbqx3Eqby8GfY1GKyg60yNl_oY68DXThb4",[5855,5858,5861,5864],{"stem":5856,"title":5857,"category":65},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fggt-und-kgv","Zusammenhang von ggT und kgV",{"stem":5859,"title":5860,"category":187},"de\u002Fformulas\u002Fmath\u002Fdiscrete-math\u002Fchinesischer-restsatz","Chinesischer Restsatz",{"stem":5862,"title":5863,"category":187},"de\u002Fformulas\u002Fmath\u002Fdiscrete-math\u002Feuklidischer-algorithmus","Euklidischer Algorithmus",{"stem":5865,"title":5866,"category":187},"de\u002Fformulas\u002Fmath\u002Fdiscrete-math\u002Frechnen-mit-kongruenzen","Rechnen mit Kongruenzen",1793824276019]