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für ",[569,1028,1029],{},"alle"," ganzen Zahlen ",[574,1032,1034,1047],{"className":1033},[577],[574,1035,1037],{"className":1036},[581],[583,1038,1039],{"xmlns":585},[587,1040,1041,1045],{},[590,1042,1043],{},[593,1044,633],{},[596,1046,633],{"encoding":598},[574,1048,1050],{"className":1049,"ariaHidden":603},[602],[574,1051,1053,1056],{"className":1052},[607],[574,1054],{"className":1055,"style":645},[611],[574,1057,633],{"className":1058},[616,617]," gilt, auch für Vielfache von ",[574,1061,1063,1076],{"className":1062},[577],[574,1064,1066],{"className":1065},[581],[583,1067,1068],{"xmlns":585},[587,1069,1070,1074],{},[590,1071,1072],{},[593,1073,565],{},[596,1075,565],{"encoding":598},[574,1077,1079],{"className":1078,"ariaHidden":603},[602],[574,1080,1082,1085],{"className":1081},[607],[574,1083],{"className":1084,"style":612},[611],[574,1086,565],{"className":1087},[616,617],".",[565,1090,1091,1092,1209,1210,1238,1239,1268,1269,1363,1364,1608,1609,1672,1673,1701],{},"Beweisidee: Die Zahlen ",[574,1093,1095,1135],{"className":1094},[577],[574,1096,1098],{"className":1097},[581],[583,1099,1100],{"xmlns":585},[587,1101,1102,1132],{},[590,1103,1104,1106,1108,1111,1113,1115,1118,1120,1122,1124,1126,1128,1130],{},[593,1105,633],{},[701,1107,915],{"separator":603},[705,1109,1110],{},"2",[593,1112,633],{},[701,1114,915],{"separator":603},[701,1116,1117],{},"…",[701,1119,915],{"separator":603},[701,1121,892],{"stretchy":891},[593,1123,565],{},[701,1125,703],{},[705,1127,707],{},[701,1129,912],{"stretchy":891},[593,1131,633],{},[596,1133,1134],{"encoding":598},"a, 2a, \\ldots, (p-1)a",[574,1136,1138,1194],{"className":1137,"ariaHidden":603},[602],[574,1139,1141,1144,1147,1150,1154,1157,1160,1163,1166,1170,1173,1176,1179,1182,1185,1188,1191],{"className":1140},[607],[574,1142],{"className":1143,"style":993},[611],[574,1145,633],{"className":1146},[616,617],[574,1148,915],{"className":1149},[1023],[574,1151],{"className":1152,"style":1153},[779],"margin-right:0.1667em;",[574,1155,1110],{"className":1156},[616],[574,1158,633],{"className":1159},[616,617],[574,1161,915],{"className":1162},[1023],[574,1164],{"className":1165,"style":1153},[779],[574,1167,1117],{"className":1168},[1169],"minner",[574,1171],{"className":1172,"style":1153},[779],[574,1174,915],{"className":1175},[1023],[574,1177],{"className":1178,"style":1153},[779],[574,1180,892],{"className":1181},[997],[574,1183,565],{"className":1184},[616,617],[574,1186],{"className":1187,"style":780},[779],[574,1189,703],{"className":1190},[772],[574,1192],{"className":1193,"style":780},[779],[574,1195,1197,1200,1203,1206],{"className":1196},[607],[574,1198],{"className":1199,"style":993},[611],[574,1201,707],{"className":1202},[616],[574,1204,912],{"className":1205},[1019],[574,1207,633],{"className":1208},[616,617]," haben modulo ",[574,1211,1213,1226],{"className":1212},[577],[574,1214,1216],{"className":1215},[581],[583,1217,1218],{"xmlns":585},[587,1219,1220,1224],{},[590,1221,1222],{},[593,1223,565],{},[596,1225,565],{"encoding":598},[574,1227,1229],{"className":1228,"ariaHidden":603},[602],[574,1230,1232,1235],{"className":1231},[607],[574,1233],{"className":1234,"style":612},[611],[574,1236,565],{"className":1237},[616,617]," paarweise verschiedene Reste ungleich ",[574,1240,1242,1256],{"className":1241},[577],[574,1243,1245],{"className":1244},[581],[583,1246,1247],{"xmlns":585},[587,1248,1249,1254],{},[590,1250,1251],{},[705,1252,1253],{},"0",[596,1255,1253],{"encoding":598},[574,1257,1259],{"className":1258,"ariaHidden":603},[602],[574,1260,1262,1265],{"className":1261},[607],[574,1263],{"className":1264,"style":793},[611],[574,1266,1253],{"className":1267},[616],", sind also eine Umordnung von ",[574,1270,1272,1302],{"className":1271},[577],[574,1273,1275],{"className":1274},[581],[583,1276,1277],{"xmlns":585},[587,1278,1279,1299],{},[590,1280,1281,1283,1285,1287,1289,1291,1293,1295,1297],{},[705,1282,707],{},[701,1284,915],{"separator":603},[705,1286,1110],{},[701,1288,915],{"separator":603},[701,1290,1117],{},[701,1292,915],{"separator":603},[593,1294,565],{},[701,1296,703],{},[705,1298,707],{},[596,1300,1301],{"encoding":598},"1, 2, \\ldots, p-1",[574,1303,1305,1354],{"className":1304,"ariaHidden":603},[602],[574,1306,1308,1312,1315,1318,1321,1324,1327,1330,1333,1336,1339,1342,1345,1348,1351],{"className":1307},[607],[574,1309],{"className":1310,"style":1311},[611],"height:0.8389em;vertical-align:-0.1944em;",[574,1313,707],{"className":1314},[616],[574,1316,915],{"className":1317},[1023],[574,1319],{"className":1320,"style":1153},[779],[574,1322,1110],{"className":1323},[616],[574,1325,915],{"className":1326},[1023],[574,1328],{"className":1329,"style":1153},[779],[574,1331,1117],{"className":1332},[1169],[574,1334],{"className":1335,"style":1153},[779],[574,1337,915],{"className":1338},[1023],[574,1340],{"className":1341,"style":1153},[779],[574,1343,565],{"className":1344},[616,617],[574,1346],{"className":1347,"style":780},[779],[574,1349,703],{"className":1350},[772],[574,1352],{"className":1353,"style":780},[779],[574,1355,1357,1360],{"className":1356},[607],[574,1358],{"className":1359,"style":793},[611],[574,1361,707],{"className":1362},[616],". Multipliziert man alle, folgt ",[574,1365,1367,1442],{"className":1366},[577],[574,1368,1370],{"className":1369},[581],[583,1371,1372],{"xmlns":585},[587,1373,1374,1439],{},[590,1375,1376,1388,1391,1393,1395,1397,1399,1401,1404,1406,1408,1410,1412,1414,1416,1418,1420,1423,1425,1433,1435,1437],{},[692,1377,1378,1380],{},[593,1379,633],{},[590,1381,1382,1384,1386],{},[593,1383,565],{},[701,1385,703],{},[705,1387,707],{},[701,1389,1390],{},"⋅",[701,1392,892],{"stretchy":891},[593,1394,565],{},[701,1396,703],{},[705,1398,707],{},[701,1400,912],{"stretchy":891},[701,1402,1403],{"stretchy":891},"!",[701,1405,881],{},[701,1407,892],{"stretchy":891},[593,1409,565],{},[701,1411,703],{},[705,1413,707],{},[701,1415,912],{"stretchy":891},[701,1417,1403],{"stretchy":891},[779,1419],{},[779,1421],{"width":1422},"0.4444em",[701,1424,892],{"stretchy":891},[590,1426,1427,1429,1431],{},[593,1428,898],{"mathvariant":897},[593,1430,901],{"mathvariant":897},[593,1432,904],{"mathvariant":897},[779,1434],{"width":907},[593,1436,565],{},[701,1438,912],{"stretchy":891},[596,1440,1441],{"encoding":598},"a^{p-1} \\cdot (p-1)! \\equiv (p-1)! \\pmod p",[574,1443,1445,1498,1519,1541,1562,1581],{"className":1444,"ariaHidden":603},[602],[574,1446,1448,1451,1489,1492,1495],{"className":1447},[607],[574,1449],{"className":1450,"style":747},[611],[574,1452,1454,1457],{"className":1453},[616],[574,1455,633],{"className":1456},[616,617],[574,1458,1460],{"className":1459},[734],[574,1461,1463],{"className":1462},[738],[574,1464,1466],{"className":1465},[742],[574,1467,1469],{"className":1468,"style":747},[746],[574,1470,1471,1474],{"style":750},[574,1472],{"className":1473,"style":755},[754],[574,1475,1477],{"className":1476},[759,760,761,762],[574,1478,1480,1483,1486],{"className":1479},[616,762],[574,1481,565],{"className":1482},[616,617,762],[574,1484,703],{"className":1485},[772,762],[574,1487,707],{"className":1488},[616,762],[574,1490],{"className":1491,"style":780},[779],[574,1493,1390],{"className":1494},[772],[574,1496],{"className":1497,"style":780},[779],[574,1499,1501,1504,1507,1510,1513,1516],{"className":1500},[607],[574,1502],{"className":1503,"style":993},[611],[574,1505,892],{"className":1506},[997],[574,1508,565],{"className":1509},[616,617],[574,1511],{"className":1512,"style":780},[779],[574,1514,703],{"className":1515},[772],[574,1517],{"className":1518,"style":780},[779],[574,1520,1522,1525,1528,1532,1535,1538],{"className":1521},[607],[574,1523],{"className":1524,"style":993},[611],[574,1526,707],{"className":1527},[616],[574,1529,1531],{"className":1530},[1019],")!",[574,1533],{"className":1534,"style":962},[779],[574,1536,881],{"className":1537},[966],[574,1539],{"className":1540,"style":962},[779],[574,1542,1544,1547,1550,1553,1556,1559],{"className":1543},[607],[574,1545],{"className":1546,"style":993},[611],[574,1548,892],{"className":1549},[997],[574,1551,565],{"className":1552},[616,617],[574,1554],{"className":1555,"style":780},[779],[574,1557,703],{"className":1558},[772],[574,1560],{"className":1561,"style":780},[779],[574,1563,1565,1568,1571,1574,1577],{"className":1564},[607],[574,1566],{"className":1567,"style":993},[611],[574,1569,707],{"className":1570},[616],[574,1572,1531],{"className":1573},[1019],[574,1575],{"className":1576},[779,982],[574,1578],{"className":1579,"style":1580},[779],"margin-right:0.4444em;",[574,1582,1584,1587,1590,1599,1602,1605],{"className":1583},[607],[574,1585],{"className":1586,"style":993},[611],[574,1588,892],{"className":1589},[997],[574,1591,1593],{"className":1592},[616],[574,1594,1596],{"className":1595},[616],[574,1597,1008],{"className":1598},[616,1007],[574,1600],{"className":1601,"style":1012},[779],[574,1603,565],{"className":1604},[616,617],[574,1606,912],{"className":1607},[1019],". Da ",[574,1610,1612,1636],{"className":1611},[577],[574,1613,1615],{"className":1614},[581],[583,1616,1617],{"xmlns":585},[587,1618,1619,1633],{},[590,1620,1621,1623,1625,1627,1629,1631],{},[701,1622,892],{"stretchy":891},[593,1624,565],{},[701,1626,703],{},[705,1628,707],{},[701,1630,912],{"stretchy":891},[701,1632,1403],{"stretchy":891},[596,1634,1635],{"encoding":598},"(p-1)!",[574,1637,1639,1660],{"className":1638,"ariaHidden":603},[602],[574,1640,1642,1645,1648,1651,1654,1657],{"className":1641},[607],[574,1643],{"className":1644,"style":993},[611],[574,1646,892],{"className":1647},[997],[574,1649,565],{"className":1650},[616,617],[574,1652],{"className":1653,"style":780},[779],[574,1655,703],{"className":1656},[772],[574,1658],{"className":1659,"style":780},[779],[574,1661,1663,1666,1669],{"className":1662},[607],[574,1664],{"className":1665,"style":993},[611],[574,1667,707],{"className":1668},[616],[574,1670,1531],{"className":1671},[1019]," zu ",[574,1674,1676,1689],{"className":1675},[577],[574,1677,1679],{"className":1678},[581],[583,1680,1681],{"xmlns":585},[587,1682,1683,1687],{},[590,1684,1685],{},[593,1686,565],{},[596,1688,565],{"encoding":598},[574,1690,1692],{"className":1691,"ariaHidden":603},[602],[574,1693,1695,1698],{"className":1694},[607],[574,1696],{"className":1697,"style":612},[611],[574,1699,565],{"className":1700},[616,617]," teilerfremd ist, darf man kürzen.",[565,1703,1704],{},"Anwendungen:",[1706,1707,1708,1823],"ul",{},[1709,1710,1711,1714,1715,1769,1770,1822],"li",{},[569,1712,1713],{},"Große Potenzen reduzieren:"," Ist ",[574,1716,1718,1737],{"className":1717},[577],[574,1719,1721],{"className":1720},[581],[583,1722,1723],{"xmlns":585},[587,1724,1725,1734],{},[590,1726,1727,1729,1732],{},[593,1728,565],{},[701,1730,1731],{},"∤",[593,1733,633],{},[596,1735,1736],{"encoding":598},"p \\nmid a",[574,1738,1740,1760],{"className":1739,"ariaHidden":603},[602],[574,1741,1743,1747,1750,1753,1757],{"className":1742},[607],[574,1744],{"className":1745,"style":1746},[611],"height:0.9925em;vertical-align:-0.2514em;",[574,1748,565],{"className":1749},[616,617],[574,1751],{"className":1752,"style":962},[779],[574,1754,1731],{"className":1755},[966,1756],"amsrm",[574,1758],{"className":1759,"style":962},[779],[574,1761,1763,1766],{"className":1762},[607],[574,1764],{"className":1765,"style":645},[611],[574,1767,633],{"className":1768},[616,617],", darf man Exponenten modulo ",[574,1771,1773,1791],{"className":1772},[577],[574,1774,1776],{"className":1775},[581],[583,1777,1778],{"xmlns":585},[587,1779,1780,1788],{},[590,1781,1782,1784,1786],{},[593,1783,565],{},[701,1785,703],{},[705,1787,707],{},[596,1789,1790],{"encoding":598},"p - 1",[574,1792,1794,1813],{"className":1793,"ariaHidden":603},[602],[574,1795,1797,1801,1804,1807,1810],{"className":1796},[607],[574,1798],{"className":1799,"style":1800},[611],"height:0.7778em;vertical-align:-0.1944em;",[574,1802,565],{"className":1803},[616,617],[574,1805],{"className":1806,"style":780},[779],[574,1808,703],{"className":1809},[772],[574,1811],{"className":1812,"style":780},[779],[574,1814,1816,1819],{"className":1815},[607],[574,1817],{"className":1818,"style":793},[611],[574,1820,707],{"className":1821},[616]," verkleinern.",[1709,1824,1825,1828,1829,2019,2020,2048,2049,2137,2138,2166,2167,2170],{},[569,1826,1827],{},"Primzahltest:"," Gilt ",[574,1830,1832,1882],{"className":1831},[577],[574,1833,1835],{"className":1834},[581],[583,1836,1837],{"xmlns":585},[587,1838,1839,1879],{},[590,1840,1841,1854,1857,1859,1861,1863,1865,1873,1875,1877],{},[692,1842,1843,1845],{},[593,1844,633],{},[590,1846,1847,1850,1852],{},[593,1848,1849],{},"n",[701,1851,703],{},[705,1853,707],{},[701,1855,1856],{},"≢",[705,1858,707],{},[779,1860],{},[779,1862],{"width":1422},[701,1864,892],{"stretchy":891},[590,1866,1867,1869,1871],{},[593,1868,898],{"mathvariant":897},[593,1870,901],{"mathvariant":897},[593,1872,904],{"mathvariant":897},[779,1874],{"width":907},[593,1876,1849],{},[701,1878,912],{"stretchy":891},[596,1880,1881],{"encoding":598},"a^{n-1} \\not\\equiv 1 \\pmod n",[574,1883,1885,1977,1992],{"className":1884,"ariaHidden":603},[602],[574,1886,1888,1892,1930,1933,1967,1971,1974],{"className":1887},[607],[574,1889],{"className":1890,"style":1891},[611],"height:1.0085em;vertical-align:-0.1944em;",[574,1893,1895,1898],{"className":1894},[616],[574,1896,633],{"className":1897},[616,617],[574,1899,1901],{"className":1900},[734],[574,1902,1904],{"className":1903},[738],[574,1905,1907],{"className":1906},[742],[574,1908,1910],{"className":1909,"style":747},[746],[574,1911,1912,1915],{"style":750},[574,1913],{"className":1914,"style":755},[754],[574,1916,1918],{"className":1917},[759,760,761,762],[574,1919,1921,1924,1927],{"className":1920},[616,762],[574,1922,1849],{"className":1923},[616,617,762],[574,1925,703],{"className":1926},[772,762],[574,1928,707],{"className":1929},[616,762],[574,1931],{"className":1932,"style":962},[779],[574,1934,1936],{"className":1935},[966],[574,1937,1940],{"className":1938},[616,1939],"vbox",[574,1941,1944],{"className":1942},[1943],"thinbox",[574,1945,1948,1952,1963],{"className":1946},[1947],"rlap",[574,1949],{"className":1950,"style":1951},[611],"height:0.8889em;vertical-align:-0.1944em;",[574,1953,1956],{"className":1954},[1955],"inner",[574,1957,1959],{"className":1958},[616],[574,1960,1962],{"className":1961},[966],"",[574,1964],{"className":1965},[1966],"fix",[574,1968],{"className":1969},[779,1970],"nobreak",[574,1972,881],{"className":1973},[966],[574,1975],{"className":1976,"style":962},[779],[574,1978,1980,1983,1986,1989],{"className":1979},[607],[574,1981],{"className":1982,"style":793},[611],[574,1984,707],{"className":1985},[616],[574,1987],{"className":1988},[779,982],[574,1990],{"className":1991,"style":1580},[779],[574,1993,1995,1998,2001,2010,2013,2016],{"className":1994},[607],[574,1996],{"className":1997,"style":993},[611],[574,1999,892],{"className":2000},[997],[574,2002,2004],{"className":2003},[616],[574,2005,2007],{"className":2006},[616],[574,2008,1008],{"className":2009},[616,1007],[574,2011],{"className":2012,"style":1012},[779],[574,2014,1849],{"className":2015},[616,617],[574,2017,912],{"className":2018},[1019]," für ein ",[574,2021,2023,2036],{"className":2022},[577],[574,2024,2026],{"className":2025},[581],[583,2027,2028],{"xmlns":585},[587,2029,2030,2034],{},[590,2031,2032],{},[593,2033,633],{},[596,2035,633],{"encoding":598},[574,2037,2039],{"className":2038,"ariaHidden":603},[602],[574,2040,2042,2045],{"className":2041},[607],[574,2043],{"className":2044,"style":645},[611],[574,2046,633],{"className":2047},[616,617]," mit ",[574,2050,2052,2085],{"className":2051},[577],[574,2053,2055],{"className":2054},[581],[583,2056,2057],{"xmlns":585},[587,2058,2059,2082],{},[590,2060,2061,2064,2067,2069,2071,2073,2075,2077,2080],{},[593,2062,2063],{"mathvariant":897},"ggT",[701,2065,2066],{},"⁡",[701,2068,892],{"stretchy":891},[593,2070,633],{},[701,2072,915],{"separator":603},[593,2074,1849],{},[701,2076,912],{"stretchy":891},[701,2078,2079],{},"=",[705,2081,707],{},[596,2083,2084],{"encoding":598},"\\operatorname{ggT}(a, n) = 1",[574,2086,2088,2128],{"className":2087,"ariaHidden":603},[602],[574,2089,2091,2094,2101,2104,2107,2110,2113,2116,2119,2122,2125],{"className":2090},[607],[574,2092],{"className":2093,"style":993},[611],[574,2095,2098],{"className":2096},[2097],"mop",[574,2099,2063],{"className":2100},[616,1007],[574,2102,892],{"className":2103},[997],[574,2105,633],{"className":2106},[616,617],[574,2108,915],{"className":2109},[1023],[574,2111],{"className":2112,"style":1153},[779],[574,2114,1849],{"className":2115},[616,617],[574,2117,912],{"className":2118},[1019],[574,2120],{"className":2121,"style":962},[779],[574,2123,2079],{"className":2124},[966],[574,2126],{"className":2127,"style":962},[779],[574,2129,2131,2134],{"className":2130},[607],[574,2132],{"className":2133,"style":793},[611],[574,2135,707],{"className":2136},[616],", dann ist ",[574,2139,2141,2154],{"className":2140},[577],[574,2142,2144],{"className":2143},[581],[583,2145,2146],{"xmlns":585},[587,2147,2148,2152],{},[590,2149,2150],{},[593,2151,1849],{},[596,2153,1849],{"encoding":598},[574,2155,2157],{"className":2156,"ariaHidden":603},[602],[574,2158,2160,2163],{"className":2159},[607],[574,2161],{"className":2162,"style":645},[611],[574,2164,1849],{"className":2165},[616,617]," sicher ",[569,2168,2169],{},"keine"," Primzahl.",[565,2172,2173,2174,1088],{},"Der Satz ist ein Spezialfall des Satzes von Euler, denn für Primzahlen gilt ",[574,2175,2177,2206],{"className":2176},[577],[574,2178,2180],{"className":2179},[581],[583,2181,2182],{"xmlns":585},[587,2183,2184,2203],{},[590,2185,2186,2189,2191,2193,2195,2197,2199,2201],{},[593,2187,2188],{},"φ",[701,2190,892],{"stretchy":891},[593,2192,565],{},[701,2194,912],{"stretchy":891},[701,2196,2079],{},[593,2198,565],{},[701,2200,703],{},[705,2202,707],{},[596,2204,2205],{"encoding":598},"\\varphi(p) = p - 1",[574,2207,2209,2236,2254],{"className":2208,"ariaHidden":603},[602],[574,2210,2212,2215,2218,2221,2224,2227,2230,2233],{"className":2211},[607],[574,2213],{"className":2214,"style":993},[611],[574,2216,2188],{"className":2217},[616,617],[574,2219,892],{"className":2220},[997],[574,2222,565],{"className":2223},[616,617],[574,2225,912],{"className":2226},[1019],[574,2228],{"className":2229,"style":962},[779],[574,2231,2079],{"className":2232},[966],[574,2234],{"className":2235,"style":962},[779],[574,2237,2239,2242,2245,2248,2251],{"className":2238},[607],[574,2240],{"className":2241,"style":1800},[611],[574,2243,565],{"className":2244},[616,617],[574,2246],{"className":2247,"style":780},[779],[574,2249,703],{"className":2250},[772],[574,2252],{"className":2253,"style":780},[779],[574,2255,2257,2260],{"className":2256},[607],[574,2258],{"className":2259,"style":793},[611],[574,2261,707],{"className":2262},[616],[560,2264,2266],{"id":2265},"beispiele","Beispiele",[565,2268,2269,2367,2368,2503,2504,2655,2656,2753],{},[569,2270,2271,2272,2336,2337,2366],{},"Rest von ",[574,2273,2275,2295],{"className":2274},[577],[574,2276,2278],{"className":2277},[581],[583,2279,2280],{"xmlns":585},[587,2281,2282,2292],{},[590,2283,2284],{},[692,2285,2286,2289],{},[705,2287,2288],{},"3",[705,2290,2291],{},"100",[596,2293,2294],{"encoding":598},"3^{100}",[574,2296,2298],{"className":2297,"ariaHidden":603},[602],[574,2299,2301,2304],{"className":2300},[607],[574,2302],{"className":2303,"style":747},[611],[574,2305,2307,2310],{"className":2306},[616],[574,2308,2288],{"className":2309},[616],[574,2311,2313],{"className":2312},[734],[574,2314,2316],{"className":2315},[738],[574,2317,2319],{"className":2318},[742],[574,2320,2322],{"className":2321,"style":747},[746],[574,2323,2324,2327],{"style":750},[574,2325],{"className":2326,"style":755},[754],[574,2328,2330],{"className":2329},[759,760,761,762],[574,2331,2333],{"className":2332},[616,762],[574,2334,2291],{"className":2335},[616,762]," modulo ",[574,2338,2340,2354],{"className":2339},[577],[574,2341,2343],{"className":2342},[581],[583,2344,2345],{"xmlns":585},[587,2346,2347,2352],{},[590,2348,2349],{},[705,2350,2351],{},"7",[596,2353,2351],{"encoding":598},[574,2355,2357],{"className":2356,"ariaHidden":603},[602],[574,2358,2360,2363],{"className":2359},[607],[574,2361],{"className":2362,"style":793},[611],[574,2364,2351],{"className":2365},[616],":"," Nach Fermat ist ",[574,2369,2371,2414],{"className":2370},[577],[574,2372,2374],{"className":2373},[581],[583,2375,2376],{"xmlns":585},[587,2377,2378,2411],{},[590,2379,2380,2387,2389,2391,2393,2395,2397,2405,2407,2409],{},[692,2381,2382,2384],{},[705,2383,2288],{},[705,2385,2386],{},"6",[701,2388,881],{},[705,2390,707],{},[779,2392],{},[779,2394],{"width":1422},[701,2396,892],{"stretchy":891},[590,2398,2399,2401,2403],{},[593,2400,898],{"mathvariant":897},[593,2402,901],{"mathvariant":897},[593,2404,904],{"mathvariant":897},[779,2406],{"width":907},[705,2408,2351],{},[701,2410,912],{"stretchy":891},[596,2412,2413],{"encoding":598},"3^6 \\equiv 1 \\pmod 7",[574,2415,2417,2461,2476],{"className":2416,"ariaHidden":603},[602],[574,2418,2420,2423,2452,2455,2458],{"className":2419},[607],[574,2421],{"className":2422,"style":747},[611],[574,2424,2426,2429],{"className":2425},[616],[574,2427,2288],{"className":2428},[616],[574,2430,2432],{"className":2431},[734],[574,2433,2435],{"className":2434},[738],[574,2436,2438],{"className":2437},[742],[574,2439,2441],{"className":2440,"style":747},[746],[574,2442,2443,2446],{"style":750},[574,2444],{"className":2445,"style":755},[754],[574,2447,2449],{"className":2448},[759,760,761,762],[574,2450,2386],{"className":2451},[616,762],[574,2453],{"className":2454,"style":962},[779],[574,2456,881],{"className":2457},[966],[574,2459],{"className":2460,"style":962},[779],[574,2462,2464,2467,2470,2473],{"className":2463},[607],[574,2465],{"className":2466,"style":793},[611],[574,2468,707],{"className":2469},[616],[574,2471],{"className":2472},[779,982],[574,2474],{"className":2475,"style":1580},[779],[574,2477,2479,2482,2485,2494,2497,2500],{"className":2478},[607],[574,2480],{"className":2481,"style":993},[611],[574,2483,892],{"className":2484},[997],[574,2486,2488],{"className":2487},[616],[574,2489,2491],{"className":2490},[616],[574,2492,1008],{"className":2493},[616,1007],[574,2495],{"className":2496,"style":1012},[779],[574,2498,2351],{"className":2499},[616],[574,2501,912],{"className":2502},[1019]," (Probe: ",[574,2505,2507,2544],{"className":2506},[577],[574,2508,2510],{"className":2509},[581],[583,2511,2512],{"xmlns":585},[587,2513,2514,2541],{},[590,2515,2516,2522,2524,2527,2529,2532,2534,2536,2539],{},[692,2517,2518,2520],{},[705,2519,2288],{},[705,2521,2386],{},[701,2523,2079],{},[705,2525,2526],{},"729",[701,2528,2079],{},[705,2530,2531],{},"104",[701,2533,1390],{},[705,2535,2351],{},[701,2537,2538],{},"+",[705,2540,707],{},[596,2542,2543],{"encoding":598},"3^6 = 729 = 104 \\cdot 7 + 1",[574,2545,2547,2591,2609,2627,2646],{"className":2546,"ariaHidden":603},[602],[574,2548,2550,2553,2582,2585,2588],{"className":2549},[607],[574,2551],{"className":2552,"style":747},[611],[574,2554,2556,2559],{"className":2555},[616],[574,2557,2288],{"className":2558},[616],[574,2560,2562],{"className":2561},[734],[574,2563,2565],{"className":2564},[738],[574,2566,2568],{"className":2567},[742],[574,2569,2571],{"className":2570,"style":747},[746],[574,2572,2573,2576],{"style":750},[574,2574],{"className":2575,"style":755},[754],[574,2577,2579],{"className":2578},[759,760,761,762],[574,2580,2386],{"className":2581},[616,762],[574,2583],{"className":2584,"style":962},[779],[574,2586,2079],{"className":2587},[966],[574,2589],{"className":2590,"style":962},[779],[574,2592,2594,2597,2600,2603,2606],{"className":2593},[607],[574,2595],{"className":2596,"style":793},[611],[574,2598,2526],{"className":2599},[616],[574,2601],{"className":2602,"style":962},[779],[574,2604,2079],{"className":2605},[966],[574,2607],{"className":2608,"style":962},[779],[574,2610,2612,2615,2618,2621,2624],{"className":2611},[607],[574,2613],{"className":2614,"style":793},[611],[574,2616,2531],{"className":2617},[616],[574,2619],{"className":2620,"style":780},[779],[574,2622,1390],{"className":2623},[772],[574,2625],{"className":2626,"style":780},[779],[574,2628,2630,2634,2637,2640,2643],{"className":2629},[607],[574,2631],{"className":2632,"style":2633},[611],"height:0.7278em;vertical-align:-0.0833em;",[574,2635,2351],{"className":2636},[616],[574,2638],{"className":2639,"style":780},[779],[574,2641,2538],{"className":2642},[772],[574,2644],{"className":2645,"style":780},[779],[574,2647,2649,2652],{"className":2648},[607],[574,2650],{"className":2651,"style":793},[611],[574,2653,707],{"className":2654},[616],"). Mit ",[574,2657,2659,2687],{"className":2658},[577],[574,2660,2662],{"className":2661},[581],[583,2663,2664],{"xmlns":585},[587,2665,2666,2684],{},[590,2667,2668,2670,2672,2675,2677,2679,2681],{},[705,2669,2291],{},[701,2671,2079],{},[705,2673,2674],{},"16",[701,2676,1390],{},[705,2678,2386],{},[701,2680,2538],{},[705,2682,2683],{},"4",[596,2685,2686],{"encoding":598},"100 = 16 \\cdot 6 + 4",[574,2688,2690,2708,2726,2744],{"className":2689,"ariaHidden":603},[602],[574,2691,2693,2696,2699,2702,2705],{"className":2692},[607],[574,2694],{"className":2695,"style":793},[611],[574,2697,2291],{"className":2698},[616],[574,2700],{"className":2701,"style":962},[779],[574,2703,2079],{"className":2704},[966],[574,2706],{"className":2707,"style":962},[779],[574,2709,2711,2714,2717,2720,2723],{"className":2710},[607],[574,2712],{"className":2713,"style":793},[611],[574,2715,2674],{"className":2716},[616],[574,2718],{"className":2719,"style":780},[779],[574,2721,1390],{"className":2722},[772],[574,2724],{"className":2725,"style":780},[779],[574,2727,2729,2732,2735,2738,2741],{"className":2728},[607],[574,2730],{"className":2731,"style":2633},[611],[574,2733,2386],{"className":2734},[616],[574,2736],{"className":2737,"style":780},[779],[574,2739,2538],{"className":2740},[772],[574,2742],{"className":2743,"style":780},[779],[574,2745,2747,2750],{"className":2746},[607],[574,2748],{"className":2749,"style":793},[611],[574,2751,2683],{"className":2752},[616]," folgt",[574,2755,2757],{"className":2756},[859],[574,2758,2760,2837],{"className":2759},[577],[574,2761,2763],{"className":2762},[581],[583,2764,2765],{"xmlns":585,"display":868},[587,2766,2767,2834],{},[590,2768,2769,2775,2777,2793,2795,2801,2803,2805,2807,2810,2812,2814,2816,2818,2820,2828,2830,2832],{},[692,2770,2771,2773],{},[705,2772,2288],{},[705,2774,2291],{},[701,2776,2079],{},[692,2778,2779,2791],{},[590,2780,2781,2783,2789],{},[701,2782,892],{"fence":603},[692,2784,2785,2787],{},[705,2786,2288],{},[705,2788,2386],{},[701,2790,912],{"fence":603},[705,2792,2674],{},[701,2794,1390],{},[692,2796,2797,2799],{},[705,2798,2288],{},[705,2800,2683],{},[701,2802,881],{},[705,2804,707],{},[701,2806,1390],{},[705,2808,2809],{},"81",[701,2811,881],{},[705,2813,2683],{},[779,2815],{},[779,2817],{"width":888},[701,2819,892],{"stretchy":891},[590,2821,2822,2824,2826],{},[593,2823,898],{"mathvariant":897},[593,2825,901],{"mathvariant":897},[593,2827,904],{"mathvariant":897},[779,2829],{"width":907},[705,2831,2351],{},[701,2833,912],{"stretchy":891},[596,2835,2836],{"encoding":598},"3^{100} = \\left(3^6\\right)^{16} \\cdot 3^4 \\equiv 1 \\cdot 81 \\equiv 4 \\pmod 7",[574,2838,2840,2888,2983,3027,3045,3063,3078],{"className":2839,"ariaHidden":603},[602],[574,2841,2843,2847,2879,2882,2885],{"className":2842},[607],[574,2844],{"className":2845,"style":2846},[611],"height:0.8641em;",[574,2848,2850,2853],{"className":2849},[616],[574,2851,2288],{"className":2852},[616],[574,2854,2856],{"className":2855},[734],[574,2857,2859],{"className":2858},[738],[574,2860,2862],{"className":2861},[742],[574,2863,2865],{"className":2864,"style":2846},[746],[574,2866,2867,2870],{"style":949},[574,2868],{"className":2869,"style":755},[754],[574,2871,2873],{"className":2872},[759,760,761,762],[574,2874,2876],{"className":2875},[616,762],[574,2877,2291],{"className":2878},[616,762],[574,2880],{"className":2881,"style":962},[779],[574,2883,2079],{"className":2884},[966],[574,2886],{"className":2887,"style":962},[779],[574,2889,2891,2895,2974,2977,2980],{"className":2890},[607],[574,2892],{"className":2893,"style":2894},[611],"height:1.4181em;vertical-align:-0.35em;",[574,2896,2898,2946],{"className":2897},[1169],[574,2899,2901,2911,2940],{"className":2900},[1169],[574,2902,2906],{"className":2903,"style":2905},[997,2904],"delimcenter","top:0em;",[574,2907,892],{"className":2908},[2909,2910],"delimsizing","size1",[574,2912,2914,2917],{"className":2913},[616],[574,2915,2288],{"className":2916},[616],[574,2918,2920],{"className":2919},[734],[574,2921,2923],{"className":2922},[738],[574,2924,2926],{"className":2925},[742],[574,2927,2929],{"className":2928,"style":2846},[746],[574,2930,2931,2934],{"style":949},[574,2932],{"className":2933,"style":755},[754],[574,2935,2937],{"className":2936},[759,760,761,762],[574,2938,2386],{"className":2939},[616,762],[574,2941,2943],{"className":2942,"style":2905},[1019,2904],[574,2944,912],{"className":2945},[2909,2910],[574,2947,2949],{"className":2948},[734],[574,2950,2952],{"className":2951},[738],[574,2953,2955],{"className":2954},[742],[574,2956,2959],{"className":2957,"style":2958},[746],"height:1.0681em;",[574,2960,2962,2965],{"style":2961},"top:-3.317em;margin-right:0.05em;",[574,2963],{"className":2964,"style":755},[754],[574,2966,2968],{"className":2967},[759,760,761,762],[574,2969,2971],{"className":2970},[616,762],[574,2972,2674],{"className":2973},[616,762],[574,2975],{"className":2976,"style":780},[779],[574,2978,1390],{"className":2979},[772],[574,2981],{"className":2982,"style":780},[779],[574,2984,2986,2989,3018,3021,3024],{"className":2985},[607],[574,2987],{"className":2988,"style":2846},[611],[574,2990,2992,2995],{"className":2991},[616],[574,2993,2288],{"className":2994},[616],[574,2996,2998],{"className":2997},[734],[574,2999,3001],{"className":3000},[738],[574,3002,3004],{"className":3003},[742],[574,3005,3007],{"className":3006,"style":2846},[746],[574,3008,3009,3012],{"style":949},[574,3010],{"className":3011,"style":755},[754],[574,3013,3015],{"className":3014},[759,760,761,762],[574,3016,2683],{"className":3017},[616,762],[574,3019],{"className":3020,"style":962},[779],[574,3022,881],{"className":3023},[966],[574,3025],{"className":3026,"style":962},[779],[574,3028,3030,3033,3036,3039,3042],{"className":3029},[607],[574,3031],{"className":3032,"style":793},[611],[574,3034,707],{"className":3035},[616],[574,3037],{"className":3038,"style":780},[779],[574,3040,1390],{"className":3041},[772],[574,3043],{"className":3044,"style":780},[779],[574,3046,3048,3051,3054,3057,3060],{"className":3047},[607],[574,3049],{"className":3050,"style":793},[611],[574,3052,2809],{"className":3053},[616],[574,3055],{"className":3056,"style":962},[779],[574,3058,881],{"className":3059},[966],[574,3061],{"className":3062,"style":962},[779],[574,3064,3066,3069,3072,3075],{"className":3065},[607],[574,3067],{"className":3068,"style":793},[611],[574,3070,2683],{"className":3071},[616],[574,3073],{"className":3074},[779,982],[574,3076],{"className":3077,"style":986},[779],[574,3079,3081,3084,3087,3096,3099,3102],{"className":3080},[607],[574,3082],{"className":3083,"style":993},[611],[574,3085,892],{"className":3086},[997],[574,3088,3090],{"className":3089},[616],[574,3091,3093],{"className":3092},[616],[574,3094,1008],{"className":3095},[616,1007],[574,3097],{"className":3098,"style":1012},[779],[574,3100,2351],{"className":3101},[616],[574,3103,912],{"className":3104},[1019],[565,3106,3107,3139,3140,3313,3314,3342,3343,3371],{},[569,3108,3109,3138],{},[574,3110,3112,3126],{"className":3111},[577],[574,3113,3115],{"className":3114},[581],[583,3116,3117],{"xmlns":585},[587,3118,3119,3124],{},[590,3120,3121],{},[705,3122,3123],{},"15",[596,3125,3123],{"encoding":598},[574,3127,3129],{"className":3128,"ariaHidden":603},[602],[574,3130,3132,3135],{"className":3131},[607],[574,3133],{"className":3134,"style":793},[611],[574,3136,3123],{"className":3137},[616]," ist keine Primzahl:"," ",[574,3141,3143,3197],{"className":3142},[577],[574,3144,3146],{"className":3145},[581],[583,3147,3148],{"xmlns":585},[587,3149,3150,3194],{},[590,3151,3152,3159,3161,3163,3167,3170,3172,3174,3176,3178,3180,3188,3190,3192],{},[692,3153,3154,3156],{},[705,3155,1110],{},[705,3157,3158],{},"14",[701,3160,2079],{},[705,3162,2674],{},[3164,3165,3166],"mtext",{}," ",[705,3168,3169],{},"384",[701,3171,881],{},[705,3173,2683],{},[779,3175],{},[779,3177],{"width":1422},[701,3179,892],{"stretchy":891},[590,3181,3182,3184,3186],{},[593,3183,898],{"mathvariant":897},[593,3185,901],{"mathvariant":897},[593,3187,904],{"mathvariant":897},[779,3189],{"width":907},[705,3191,3123],{},[701,3193,912],{"stretchy":891},[596,3195,3196],{"encoding":598},"2^{14} = 16\\,384 \\equiv 4 \\pmod{15}",[574,3198,3200,3247,3271,3286],{"className":3199,"ariaHidden":603},[602],[574,3201,3203,3206,3238,3241,3244],{"className":3202},[607],[574,3204],{"className":3205,"style":747},[611],[574,3207,3209,3212],{"className":3208},[616],[574,3210,1110],{"className":3211},[616],[574,3213,3215],{"className":3214},[734],[574,3216,3218],{"className":3217},[738],[574,3219,3221],{"className":3220},[742],[574,3222,3224],{"className":3223,"style":747},[746],[574,3225,3226,3229],{"style":750},[574,3227],{"className":3228,"style":755},[754],[574,3230,3232],{"className":3231},[759,760,761,762],[574,3233,3235],{"className":3234},[616,762],[574,3236,3158],{"className":3237},[616,762],[574,3239],{"className":3240,"style":962},[779],[574,3242,2079],{"className":3243},[966],[574,3245],{"className":3246,"style":962},[779],[574,3248,3250,3253,3256,3259,3262,3265,3268],{"className":3249},[607],[574,3251],{"className":3252,"style":793},[611],[574,3254,2674],{"className":3255},[616],[574,3257],{"className":3258,"style":1153},[779],[574,3260,3169],{"className":3261},[616],[574,3263],{"className":3264,"style":962},[779],[574,3266,881],{"className":3267},[966],[574,3269],{"className":3270,"style":962},[779],[574,3272,3274,3277,3280,3283],{"className":3273},[607],[574,3275],{"className":3276,"style":793},[611],[574,3278,2683],{"className":3279},[616],[574,3281],{"className":3282},[779,982],[574,3284],{"className":3285,"style":1580},[779],[574,3287,3289,3292,3295,3304,3307,3310],{"className":3288},[607],[574,3290],{"className":3291,"style":993},[611],[574,3293,892],{"className":3294},[997],[574,3296,3298],{"className":3297},[616],[574,3299,3301],{"className":3300},[616],[574,3302,1008],{"className":3303},[616,1007],[574,3305],{"className":3306,"style":1012},[779],[574,3308,3123],{"className":3309},[616],[574,3311,912],{"className":3312},[1019],". Wäre ",[574,3315,3317,3330],{"className":3316},[577],[574,3318,3320],{"className":3319},[581],[583,3321,3322],{"xmlns":585},[587,3323,3324,3328],{},[590,3325,3326],{},[705,3327,3123],{},[596,3329,3123],{"encoding":598},[574,3331,3333],{"className":3332,"ariaHidden":603},[602],[574,3334,3336,3339],{"className":3335},[607],[574,3337],{"className":3338,"style":793},[611],[574,3340,3123],{"className":3341},[616]," prim, müsste der Rest ",[574,3344,3346,3359],{"className":3345},[577],[574,3347,3349],{"className":3348},[581],[583,3350,3351],{"xmlns":585},[587,3352,3353,3357],{},[590,3354,3355],{},[705,3356,707],{},[596,3358,707],{"encoding":598},[574,3360,3362],{"className":3361,"ariaHidden":603},[602],[574,3363,3365,3368],{"className":3364},[607],[574,3366],{"className":3367,"style":793},[611],[574,3369,707],{"className":3370},[616]," sein.",[560,3373,3375],{"id":3374},"typische-fehler","Typische Fehler",[1706,3377,3378,4048,4478,4852],{},[1709,3379,3380,3383,3384,3533,3534,3562,3563,3639,3640,3792,3793,4044,4045,1088],{},[569,3381,3382],{},"Die Umkehrung für wahr halten."," Aus ",[574,3385,3387,3435],{"className":3386},[577],[574,3388,3390],{"className":3389},[581],[583,3391,3392],{"xmlns":585},[587,3393,3394,3432],{},[590,3395,3396,3408,3410,3412,3414,3416,3418,3426,3428,3430],{},[692,3397,3398,3400],{},[593,3399,633],{},[590,3401,3402,3404,3406],{},[593,3403,1849],{},[701,3405,703],{},[705,3407,707],{},[701,3409,881],{},[705,3411,707],{},[779,3413],{},[779,3415],{"width":1422},[701,3417,892],{"stretchy":891},[590,3419,3420,3422,3424],{},[593,3421,898],{"mathvariant":897},[593,3423,901],{"mathvariant":897},[593,3425,904],{"mathvariant":897},[779,3427],{"width":907},[593,3429,1849],{},[701,3431,912],{"stretchy":891},[596,3433,3434],{"encoding":598},"a^{n-1} \\equiv 1 \\pmod n",[574,3436,3438,3491,3506],{"className":3437,"ariaHidden":603},[602],[574,3439,3441,3444,3482,3485,3488],{"className":3440},[607],[574,3442],{"className":3443,"style":747},[611],[574,3445,3447,3450],{"className":3446},[616],[574,3448,633],{"className":3449},[616,617],[574,3451,3453],{"className":3452},[734],[574,3454,3456],{"className":3455},[738],[574,3457,3459],{"className":3458},[742],[574,3460,3462],{"className":3461,"style":747},[746],[574,3463,3464,3467],{"style":750},[574,3465],{"className":3466,"style":755},[754],[574,3468,3470],{"className":3469},[759,760,761,762],[574,3471,3473,3476,3479],{"className":3472},[616,762],[574,3474,1849],{"className":3475},[616,617,762],[574,3477,703],{"className":3478},[772,762],[574,3480,707],{"className":3481},[616,762],[574,3483],{"className":3484,"style":962},[779],[574,3486,881],{"className":3487},[966],[574,3489],{"className":3490,"style":962},[779],[574,3492,3494,3497,3500,3503],{"className":3493},[607],[574,3495],{"className":3496,"style":793},[611],[574,3498,707],{"className":3499},[616],[574,3501],{"className":3502},[779,982],[574,3504],{"className":3505,"style":1580},[779],[574,3507,3509,3512,3515,3524,3527,3530],{"className":3508},[607],[574,3510],{"className":3511,"style":993},[611],[574,3513,892],{"className":3514},[997],[574,3516,3518],{"className":3517},[616],[574,3519,3521],{"className":3520},[616],[574,3522,1008],{"className":3523},[616,1007],[574,3525],{"className":3526,"style":1012},[779],[574,3528,1849],{"className":3529},[616,617],[574,3531,912],{"className":3532},[1019]," folgt nicht, dass ",[574,3535,3537,3550],{"className":3536},[577],[574,3538,3540],{"className":3539},[581],[583,3541,3542],{"xmlns":585},[587,3543,3544,3548],{},[590,3545,3546],{},[593,3547,1849],{},[596,3549,1849],{"encoding":598},[574,3551,3553],{"className":3552,"ariaHidden":603},[602],[574,3554,3556,3559],{"className":3555},[607],[574,3557],{"className":3558,"style":645},[611],[574,3560,1849],{"className":3561},[616,617]," prim ist. Gegenbeispiel: ",[574,3564,3566,3591],{"className":3565},[577],[574,3567,3569],{"className":3568},[581],[583,3570,3571],{"xmlns":585},[587,3572,3573,3588],{},[590,3574,3575,3578,3580,3583,3585],{},[705,3576,3577],{},"341",[701,3579,2079],{},[705,3581,3582],{},"11",[701,3584,1390],{},[705,3586,3587],{},"31",[596,3589,3590],{"encoding":598},"341 = 11 \\cdot 31",[574,3592,3594,3612,3630],{"className":3593,"ariaHidden":603},[602],[574,3595,3597,3600,3603,3606,3609],{"className":3596},[607],[574,3598],{"className":3599,"style":793},[611],[574,3601,3577],{"className":3602},[616],[574,3604],{"className":3605,"style":962},[779],[574,3607,2079],{"className":3608},[966],[574,3610],{"className":3611,"style":962},[779],[574,3613,3615,3618,3621,3624,3627],{"className":3614},[607],[574,3616],{"className":3617,"style":793},[611],[574,3619,3582],{"className":3620},[616],[574,3622],{"className":3623,"style":780},[779],[574,3625,1390],{"className":3626},[772],[574,3628],{"className":3629,"style":780},[779],[574,3631,3633,3636],{"className":3632},[607],[574,3634],{"className":3635,"style":793},[611],[574,3637,3587],{"className":3638},[616],", aber ",[574,3641,3643,3679],{"className":3642},[577],[574,3644,3646],{"className":3645},[581],[583,3647,3648],{"xmlns":585},[587,3649,3650,3676],{},[590,3651,3652,3659,3661,3664,3666,3668,3670,3672,3674],{},[692,3653,3654,3656],{},[705,3655,1110],{},[705,3657,3658],{},"10",[701,3660,2079],{},[705,3662,3663],{},"1024",[701,3665,2079],{},[705,3667,2288],{},[701,3669,1390],{},[705,3671,3577],{},[701,3673,2538],{},[705,3675,707],{},[596,3677,3678],{"encoding":598},"2^{10} = 1024 = 3 \\cdot 341 + 1",[574,3680,3682,3729,3747,3765,3783],{"className":3681,"ariaHidden":603},[602],[574,3683,3685,3688,3720,3723,3726],{"className":3684},[607],[574,3686],{"className":3687,"style":747},[611],[574,3689,3691,3694],{"className":3690},[616],[574,3692,1110],{"className":3693},[616],[574,3695,3697],{"className":3696},[734],[574,3698,3700],{"className":3699},[738],[574,3701,3703],{"className":3702},[742],[574,3704,3706],{"className":3705,"style":747},[746],[574,3707,3708,3711],{"style":750},[574,3709],{"className":3710,"style":755},[754],[574,3712,3714],{"className":3713},[759,760,761,762],[574,3715,3717],{"className":3716},[616,762],[574,3718,3658],{"className":3719},[616,762],[574,3721],{"className":3722,"style":962},[779],[574,3724,2079],{"className":3725},[966],[574,3727],{"className":3728,"style":962},[779],[574,3730,3732,3735,3738,3741,3744],{"className":3731},[607],[574,3733],{"className":3734,"style":793},[611],[574,3736,3663],{"className":3737},[616],[574,3739],{"className":3740,"style":962},[779],[574,3742,2079],{"className":3743},[966],[574,3745],{"className":3746,"style":962},[779],[574,3748,3750,3753,3756,3759,3762],{"className":3749},[607],[574,3751],{"className":3752,"style":793},[611],[574,3754,2288],{"className":3755},[616],[574,3757],{"className":3758,"style":780},[779],[574,3760,1390],{"className":3761},[772],[574,3763],{"className":3764,"style":780},[779],[574,3766,3768,3771,3774,3777,3780],{"className":3767},[607],[574,3769],{"className":3770,"style":2633},[611],[574,3772,3577],{"className":3773},[616],[574,3775],{"className":3776,"style":780},[779],[574,3778,2538],{"className":3779},[772],[574,3781],{"className":3782,"style":780},[779],[574,3784,3786,3789],{"className":3785},[607],[574,3787],{"className":3788,"style":793},[611],[574,3790,707],{"className":3791},[616],", also ",[574,3794,3796,3858],{"className":3795},[577],[574,3797,3799],{"className":3798},[581],[583,3800,3801],{"xmlns":585},[587,3802,3803,3855],{},[590,3804,3805,3812,3814,3831,3833,3835,3837,3839,3841,3849,3851,3853],{},[692,3806,3807,3809],{},[705,3808,1110],{},[705,3810,3811],{},"340",[701,3813,2079],{},[692,3815,3816,3828],{},[590,3817,3818,3820,3826],{},[701,3819,892],{"fence":603},[692,3821,3822,3824],{},[705,3823,1110],{},[705,3825,3658],{},[701,3827,912],{"fence":603},[705,3829,3830],{},"34",[701,3832,881],{},[705,3834,707],{},[779,3836],{},[779,3838],{"width":1422},[701,3840,892],{"stretchy":891},[590,3842,3843,3845,3847],{},[593,3844,898],{"mathvariant":897},[593,3846,901],{"mathvariant":897},[593,3848,904],{"mathvariant":897},[779,3850],{"width":907},[705,3852,3577],{},[701,3854,912],{"stretchy":891},[596,3856,3857],{"encoding":598},"2^{340} = \\left(2^{10}\\right)^{34} \\equiv 1 \\pmod{341}",[574,3859,3861,3908,4002,4017],{"className":3860,"ariaHidden":603},[602],[574,3862,3864,3867,3899,3902,3905],{"className":3863},[607],[574,3865],{"className":3866,"style":747},[611],[574,3868,3870,3873],{"className":3869},[616],[574,3871,1110],{"className":3872},[616],[574,3874,3876],{"className":3875},[734],[574,3877,3879],{"className":3878},[738],[574,3880,3882],{"className":3881},[742],[574,3883,3885],{"className":3884,"style":747},[746],[574,3886,3887,3890],{"style":750},[574,3888],{"className":3889,"style":755},[754],[574,3891,3893],{"className":3892},[759,760,761,762],[574,3894,3896],{"className":3895},[616,762],[574,3897,3811],{"className":3898},[616,762],[574,3900],{"className":3901,"style":962},[779],[574,3903,2079],{"className":3904},[966],[574,3906],{"className":3907,"style":962},[779],[574,3909,3911,3915,3993,3996,3999],{"className":3910},[607],[574,3912],{"className":3913,"style":3914},[611],"height:1.404em;vertical-align:-0.35em;",[574,3916,3918,3965],{"className":3917},[1169],[574,3919,3921,3927,3959],{"className":3920},[1169],[574,3922,3924],{"className":3923,"style":2905},[997,2904],[574,3925,892],{"className":3926},[2909,2910],[574,3928,3930,3933],{"className":3929},[616],[574,3931,1110],{"className":3932},[616],[574,3934,3936],{"className":3935},[734],[574,3937,3939],{"className":3938},[738],[574,3940,3942],{"className":3941},[742],[574,3943,3945],{"className":3944,"style":747},[746],[574,3946,3947,3950],{"style":750},[574,3948],{"className":3949,"style":755},[754],[574,3951,3953],{"className":3952},[759,760,761,762],[574,3954,3956],{"className":3955},[616,762],[574,3957,3658],{"className":3958},[616,762],[574,3960,3962],{"className":3961,"style":2905},[1019,2904],[574,3963,912],{"className":3964},[2909,2910],[574,3966,3968],{"className":3967},[734],[574,3969,3971],{"className":3970},[738],[574,3972,3974],{"className":3973},[742],[574,3975,3978],{"className":3976,"style":3977},[746],"height:1.054em;",[574,3979,3981,3984],{"style":3980},"top:-3.3029em;margin-right:0.05em;",[574,3982],{"className":3983,"style":755},[754],[574,3985,3987],{"className":3986},[759,760,761,762],[574,3988,3990],{"className":3989},[616,762],[574,3991,3830],{"className":3992},[616,762],[574,3994],{"className":3995,"style":962},[779],[574,3997,881],{"className":3998},[966],[574,4000],{"className":4001,"style":962},[779],[574,4003,4005,4008,4011,4014],{"className":4004},[607],[574,4006],{"className":4007,"style":793},[611],[574,4009,707],{"className":4010},[616],[574,4012],{"className":4013},[779,982],[574,4015],{"className":4016,"style":1580},[779],[574,4018,4020,4023,4026,4035,4038,4041],{"className":4019},[607],[574,4021],{"className":4022,"style":993},[611],[574,4024,892],{"className":4025},[997],[574,4027,4029],{"className":4028},[616],[574,4030,4032],{"className":4031},[616],[574,4033,1008],{"className":4034},[616,1007],[574,4036],{"className":4037,"style":1012},[779],[574,4039,3577],{"className":4040},[616],[574,4042,912],{"className":4043},[1019],". Solche Zahlen heißen ",[569,4046,4047],{},"Fermatsche Pseudoprimzahlen",[1709,4049,4050,4104,4105,4156,4157,4208,4209,4366,4367,4395,4396,1088],{},[569,4051,4052,4053,4103],{},"Die Voraussetzung ",[574,4054,4056,4073],{"className":4055},[577],[574,4057,4059],{"className":4058},[581],[583,4060,4061],{"xmlns":585},[587,4062,4063,4071],{},[590,4064,4065,4067,4069],{},[593,4066,565],{},[701,4068,1731],{},[593,4070,633],{},[596,4072,1736],{"encoding":598},[574,4074,4076,4094],{"className":4075,"ariaHidden":603},[602],[574,4077,4079,4082,4085,4088,4091],{"className":4078},[607],[574,4080],{"className":4081,"style":1746},[611],[574,4083,565],{"className":4084},[616,617],[574,4086],{"className":4087,"style":962},[779],[574,4089,1731],{"className":4090},[966,1756],[574,4092],{"className":4093,"style":962},[779],[574,4095,4097,4100],{"className":4096},[607],[574,4098],{"className":4099,"style":645},[611],[574,4101,633],{"className":4102},[616,617]," vergessen."," Für ",[574,4106,4108,4126],{"className":4107},[577],[574,4109,4111],{"className":4110},[581],[583,4112,4113],{"xmlns":585},[587,4114,4115,4123],{},[590,4116,4117,4119,4121],{},[593,4118,633],{},[701,4120,2079],{},[705,4122,2386],{},[596,4124,4125],{"encoding":598},"a = 6",[574,4127,4129,4147],{"className":4128,"ariaHidden":603},[602],[574,4130,4132,4135,4138,4141,4144],{"className":4131},[607],[574,4133],{"className":4134,"style":645},[611],[574,4136,633],{"className":4137},[616,617],[574,4139],{"className":4140,"style":962},[779],[574,4142,2079],{"className":4143},[966],[574,4145],{"className":4146,"style":962},[779],[574,4148,4150,4153],{"className":4149},[607],[574,4151],{"className":4152,"style":793},[611],[574,4154,2386],{"className":4155},[616]," und ",[574,4158,4160,4178],{"className":4159},[577],[574,4161,4163],{"className":4162},[581],[583,4164,4165],{"xmlns":585},[587,4166,4167,4175],{},[590,4168,4169,4171,4173],{},[593,4170,565],{},[701,4172,2079],{},[705,4174,2288],{},[596,4176,4177],{"encoding":598},"p = 3",[574,4179,4181,4199],{"className":4180,"ariaHidden":603},[602],[574,4182,4184,4187,4190,4193,4196],{"className":4183},[607],[574,4185],{"className":4186,"style":612},[611],[574,4188,565],{"className":4189},[616,617],[574,4191],{"className":4192,"style":962},[779],[574,4194,2079],{"className":4195},[966],[574,4197],{"className":4198,"style":962},[779],[574,4200,4202,4205],{"className":4201},[607],[574,4203],{"className":4204,"style":793},[611],[574,4206,2288],{"className":4207},[616]," ist ",[574,4210,4212,4259],{"className":4211},[577],[574,4213,4215],{"className":4214},[581],[583,4216,4217],{"xmlns":585},[587,4218,4219,4256],{},[590,4220,4221,4227,4229,4232,4234,4236,4238,4240,4242,4250,4252,4254],{},[692,4222,4223,4225],{},[705,4224,2386],{},[705,4226,1110],{},[701,4228,2079],{},[705,4230,4231],{},"36",[701,4233,881],{},[705,4235,1253],{},[779,4237],{},[779,4239],{"width":1422},[701,4241,892],{"stretchy":891},[590,4243,4244,4246,4248],{},[593,4245,898],{"mathvariant":897},[593,4247,901],{"mathvariant":897},[593,4249,904],{"mathvariant":897},[779,4251],{"width":907},[705,4253,2288],{},[701,4255,912],{"stretchy":891},[596,4257,4258],{"encoding":598},"6^2 = 36 \\equiv 0 \\pmod 3",[574,4260,4262,4306,4324,4339],{"className":4261,"ariaHidden":603},[602],[574,4263,4265,4268,4297,4300,4303],{"className":4264},[607],[574,4266],{"className":4267,"style":747},[611],[574,4269,4271,4274],{"className":4270},[616],[574,4272,2386],{"className":4273},[616],[574,4275,4277],{"className":4276},[734],[574,4278,4280],{"className":4279},[738],[574,4281,4283],{"className":4282},[742],[574,4284,4286],{"className":4285,"style":747},[746],[574,4287,4288,4291],{"style":750},[574,4289],{"className":4290,"style":755},[754],[574,4292,4294],{"className":4293},[759,760,761,762],[574,4295,1110],{"className":4296},[616,762],[574,4298],{"className":4299,"style":962},[779],[574,4301,2079],{"className":4302},[966],[574,4304],{"className":4305,"style":962},[779],[574,4307,4309,4312,4315,4318,4321],{"className":4308},[607],[574,4310],{"className":4311,"style":793},[611],[574,4313,4231],{"className":4314},[616],[574,4316],{"className":4317,"style":962},[779],[574,4319,881],{"className":4320},[966],[574,4322],{"className":4323,"style":962},[779],[574,4325,4327,4330,4333,4336],{"className":4326},[607],[574,4328],{"className":4329,"style":793},[611],[574,4331,1253],{"className":4332},[616],[574,4334],{"className":4335},[779,982],[574,4337],{"className":4338,"style":1580},[779],[574,4340,4342,4345,4348,4357,4360,4363],{"className":4341},[607],[574,4343],{"className":4344,"style":993},[611],[574,4346,892],{"className":4347},[997],[574,4349,4351],{"className":4350},[616],[574,4352,4354],{"className":4353},[616],[574,4355,1008],{"className":4356},[616,1007],[574,4358],{"className":4359,"style":1012},[779],[574,4361,2288],{"className":4362},[616],[574,4364,912],{"className":4365},[1019],", nicht ",[574,4368,4370,4383],{"className":4369},[577],[574,4371,4373],{"className":4372},[581],[583,4374,4375],{"xmlns":585},[587,4376,4377,4381],{},[590,4378,4379],{},[705,4380,707],{},[596,4382,707],{"encoding":598},[574,4384,4386],{"className":4385,"ariaHidden":603},[602],[574,4387,4389,4392],{"className":4388},[607],[574,4390],{"className":4391,"style":793},[611],[574,4393,707],{"className":4394},[616],". Ohne Voraussetzung gilt nur ",[574,4397,4399,4421],{"className":4398},[577],[574,4400,4402],{"className":4401},[581],[583,4403,4404],{"xmlns":585},[587,4405,4406,4418],{},[590,4407,4408,4414,4416],{},[692,4409,4410,4412],{},[593,4411,633],{},[593,4413,565],{},[701,4415,881],{},[593,4417,633],{},[596,4419,4420],{"encoding":598},"a^p \\equiv a",[574,4422,4424,4469],{"className":4423,"ariaHidden":603},[602],[574,4425,4427,4431,4460,4463,4466],{"className":4426},[607],[574,4428],{"className":4429,"style":4430},[611],"height:0.6644em;",[574,4432,4434,4437],{"className":4433},[616],[574,4435,633],{"className":4436},[616,617],[574,4438,4440],{"className":4439},[734],[574,4441,4443],{"className":4442},[738],[574,4444,4446],{"className":4445},[742],[574,4447,4449],{"className":4448,"style":4430},[746],[574,4450,4451,4454],{"style":750},[574,4452],{"className":4453,"style":755},[754],[574,4455,4457],{"className":4456},[759,760,761,762],[574,4458,565],{"className":4459},[616,617,762],[574,4461],{"className":4462,"style":962},[779],[574,4464,881],{"className":4465},[966],[574,4467],{"className":4468,"style":962},[779],[574,4470,4472,4475],{"className":4471},[607],[574,4473],{"className":4474,"style":645},[611],[574,4476,633],{"className":4477},[616,617],[1709,4479,4480,4563,4564,2336,4625,4653,4654,4366,4755,1088],{},[569,4481,4482,4483,4511,4512,4562],{},"Den Exponenten modulo ",[574,4484,4486,4499],{"className":4485},[577],[574,4487,4489],{"className":4488},[581],[583,4490,4491],{"xmlns":585},[587,4492,4493,4497],{},[590,4494,4495],{},[593,4496,565],{},[596,4498,565],{"encoding":598},[574,4500,4502],{"className":4501,"ariaHidden":603},[602],[574,4503,4505,4508],{"className":4504},[607],[574,4506],{"className":4507,"style":612},[611],[574,4509,565],{"className":4510},[616,617]," statt modulo ",[574,4513,4515,4532],{"className":4514},[577],[574,4516,4518],{"className":4517},[581],[583,4519,4520],{"xmlns":585},[587,4521,4522,4530],{},[590,4523,4524,4526,4528],{},[593,4525,565],{},[701,4527,703],{},[705,4529,707],{},[596,4531,1790],{"encoding":598},[574,4533,4535,4553],{"className":4534,"ariaHidden":603},[602],[574,4536,4538,4541,4544,4547,4550],{"className":4537},[607],[574,4539],{"className":4540,"style":1800},[611],[574,4542,565],{"className":4543},[616,617],[574,4545],{"className":4546,"style":780},[779],[574,4548,703],{"className":4549},[772],[574,4551],{"className":4552,"style":780},[779],[574,4554,4556,4559],{"className":4555},[607],[574,4557],{"className":4558,"style":793},[611],[574,4560,707],{"className":4561},[616]," reduzieren."," Bei ",[574,4565,4567,4584],{"className":4566},[577],[574,4568,4570],{"className":4569},[581],[583,4571,4572],{"xmlns":585},[587,4573,4574,4582],{},[590,4575,4576],{},[692,4577,4578,4580],{},[705,4579,2288],{},[705,4581,2291],{},[596,4583,2294],{"encoding":598},[574,4585,4587],{"className":4586,"ariaHidden":603},[602],[574,4588,4590,4593],{"className":4589},[607],[574,4591],{"className":4592,"style":747},[611],[574,4594,4596,4599],{"className":4595},[616],[574,4597,2288],{"className":4598},[616],[574,4600,4602],{"className":4601},[734],[574,4603,4605],{"className":4604},[738],[574,4606,4608],{"className":4607},[742],[574,4609,4611],{"className":4610,"style":747},[746],[574,4612,4613,4616],{"style":750},[574,4614],{"className":4615,"style":755},[754],[574,4617,4619],{"className":4618},[759,760,761,762],[574,4620,4622],{"className":4621},[616,762],[574,4623,2291],{"className":4624},[616,762],[574,4626,4628,4641],{"className":4627},[577],[574,4629,4631],{"className":4630},[581],[583,4632,4633],{"xmlns":585},[587,4634,4635,4639],{},[590,4636,4637],{},[705,4638,2351],{},[596,4640,2351],{"encoding":598},[574,4642,4644],{"className":4643,"ariaHidden":603},[602],[574,4645,4647,4650],{"className":4646},[607],[574,4648],{"className":4649,"style":793},[611],[574,4651,2351],{"className":4652},[616]," zählt ",[574,4655,4657,4693],{"className":4656},[577],[574,4658,4660],{"className":4659},[581],[583,4661,4662],{"xmlns":585},[587,4663,4664,4690],{},[590,4665,4666,4668,4671,4682,4684,4686,4688],{},[705,4667,2291],{},[3164,4669,4670],{}," ",[701,4672,4674],{"lspace":4673,"rspace":4673},"0.22em",[590,4675,4676,4678,4680],{},[593,4677,898],{"mathvariant":897},[593,4679,901],{"mathvariant":897},[593,4681,904],{"mathvariant":897},[3164,4683,4670],{},[705,4685,2386],{},[701,4687,2079],{},[705,4689,2683],{},[596,4691,4692],{"encoding":598},"100 \\bmod 6 = 4",[574,4694,4696,4728,4746],{"className":4695,"ariaHidden":603},[602],[574,4697,4699,4703,4706,4710,4713,4722,4725],{"className":4698},[607],[574,4700],{"className":4701,"style":4702},[611],"height:0.6944em;",[574,4704,2291],{"className":4705},[616],[574,4707],{"className":4708,"style":4709},[779],"margin-right:0.0556em;",[574,4711],{"className":4712,"style":780},[779],[574,4714,4716],{"className":4715},[772],[574,4717,4719],{"className":4718},[616],[574,4720,1008],{"className":4721},[616,1007],[574,4723],{"className":4724,"style":4709},[779],[574,4726],{"className":4727,"style":780},[779],[574,4729,4731,4734,4737,4740,4743],{"className":4730},[607],[574,4732],{"className":4733,"style":793},[611],[574,4735,2386],{"className":4736},[616],[574,4738],{"className":4739,"style":962},[779],[574,4741,2079],{"className":4742},[966],[574,4744],{"className":4745,"style":962},[779],[574,4747,4749,4752],{"className":4748},[607],[574,4750],{"className":4751,"style":793},[611],[574,4753,2683],{"className":4754},[616],[574,4756,4758,4792],{"className":4757},[577],[574,4759,4761],{"className":4760},[581],[583,4762,4763],{"xmlns":585},[587,4764,4765,4789],{},[590,4766,4767,4769,4771,4781,4783,4785,4787],{},[705,4768,2291],{},[3164,4770,4670],{},[701,4772,4773],{"lspace":4673,"rspace":4673},[590,4774,4775,4777,4779],{},[593,4776,898],{"mathvariant":897},[593,4778,901],{"mathvariant":897},[593,4780,904],{"mathvariant":897},[3164,4782,4670],{},[705,4784,2351],{},[701,4786,2079],{},[705,4788,1110],{},[596,4790,4791],{"encoding":598},"100 \\bmod 7 = 2",[574,4793,4795,4825,4843],{"className":4794,"ariaHidden":603},[602],[574,4796,4798,4801,4804,4807,4810,4819,4822],{"className":4797},[607],[574,4799],{"className":4800,"style":4702},[611],[574,4802,2291],{"className":4803},[616],[574,4805],{"className":4806,"style":4709},[779],[574,4808],{"className":4809,"style":780},[779],[574,4811,4813],{"className":4812},[772],[574,4814,4816],{"className":4815},[616],[574,4817,1008],{"className":4818},[616,1007],[574,4820],{"className":4821,"style":4709},[779],[574,4823],{"className":4824,"style":780},[779],[574,4826,4828,4831,4834,4837,4840],{"className":4827},[607],[574,4829],{"className":4830,"style":793},[611],[574,4832,2351],{"className":4833},[616],[574,4835],{"className":4836,"style":962},[779],[574,4838,2079],{"className":4839},[966],[574,4841],{"className":4842,"style":962},[779],[574,4844,4846,4849],{"className":4845},[607],[574,4847],{"className":4848,"style":793},[611],[574,4850,1110],{"className":4851},[616],[1709,4853,4854,4104,4857,4908,4909,4976,4977,1088],{},[569,4855,4856],{},"Den Satz für zusammengesetzte Moduln verwenden.",[574,4858,4860,4878],{"className":4859},[577],[574,4861,4863],{"className":4862},[581],[583,4864,4865],{"xmlns":585},[587,4866,4867,4875],{},[590,4868,4869,4871,4873],{},[593,4870,898],{},[701,4872,2079],{},[705,4874,3123],{},[596,4876,4877],{"encoding":598},"m = 15",[574,4879,4881,4899],{"className":4880,"ariaHidden":603},[602],[574,4882,4884,4887,4890,4893,4896],{"className":4883},[607],[574,4885],{"className":4886,"style":645},[611],[574,4888,898],{"className":4889},[616,617],[574,4891],{"className":4892,"style":962},[779],[574,4894,2079],{"className":4895},[966],[574,4897],{"className":4898,"style":962},[779],[574,4900,4902,4905],{"className":4901},[607],[574,4903],{"className":4904,"style":793},[611],[574,4906,3123],{"className":4907},[616]," braucht man den Satz von Euler mit ",[574,4910,4912,4937],{"className":4911},[577],[574,4913,4915],{"className":4914},[581],[583,4916,4917],{"xmlns":585},[587,4918,4919,4934],{},[590,4920,4921,4923,4925,4927,4929,4931],{},[593,4922,2188],{},[701,4924,892],{"stretchy":891},[705,4926,3123],{},[701,4928,912],{"stretchy":891},[701,4930,2079],{},[705,4932,4933],{},"8",[596,4935,4936],{"encoding":598},"\\varphi(15) = 8",[574,4938,4940,4967],{"className":4939,"ariaHidden":603},[602],[574,4941,4943,4946,4949,4952,4955,4958,4961,4964],{"className":4942},[607],[574,4944],{"className":4945,"style":993},[611],[574,4947,2188],{"className":4948},[616,617],[574,4950,892],{"className":4951},[997],[574,4953,3123],{"className":4954},[616],[574,4956,912],{"className":4957},[1019],[574,4959],{"className":4960,"style":962},[779],[574,4962,2079],{"className":4963},[966],[574,4965],{"className":4966,"style":962},[779],[574,4968,4970,4973],{"className":4969},[607],[574,4971],{"className":4972,"style":793},[611],[574,4974,4933],{"className":4975},[616],", nicht den Exponenten 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class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan style=\"white-space: nowrap\">\u003Cspan class=\"katex\">Primzahl\u003C\u002Fspan>\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">,\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:0.3em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\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>\u003Cmi>a\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 \\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:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\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>\u003Cmi>p\u003C\u002Fmi>\u003Cmo>∤\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p \\nmid a\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:0.9925em;vertical-align:-0.2514em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel amsrm\">∤\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","fermat-little-theorem","a^{p-1} \\equiv 1 \\pmod p","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsup>\u003Cmi>a\u003C\u002Fmi>\u003Cmrow>\u003Cmi>p\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmrow>\u003C\u002Fmsup>\u003Cmo>≡\u003C\u002Fmo>\u003Cmn>1\u003C\u002Fmn>\u003Cmspace>\u003C\u002Fmspace>\u003Cmspace width=\"1em\"\u002F>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmrow>\u003Cmi 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class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathrm\">mod\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.3333em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","university",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fdiscrete-math\u002Fkleiner-satz-von-fermat",[],[5070,5071,5072],"euler-theorem","modular-arithmetic","prime-factorization",{"title":548,"description":5006},"de\u002Fformulas\u002Fmath\u002Fdiscrete-math\u002Fkleiner-satz-von-fermat","Für jede Primzahl p und jede nicht durch p teilbare Zahl a lässt a hoch p−1 bei Division durch p den Rest 1.",[5077,5078,5079,5080],"primzahl","kongruenz","potenz modulo","zahlentheorie",[5082,5085],{"symbol":565,"meaning":5083,"symbolHtml":5084},"Primzahl, die als Modul 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encoding=\"application\u002Fx-tex\">a\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:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","rfPZqefISBiIExAG-0Xl8b0ZGj-YgPeMHQMLaeqCJPM",[5090,5093,5096],{"stem":5091,"title":5092,"category":65},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fprimfaktorzerlegung","Primfaktorzerlegung",{"stem":5094,"title":5095,"category":187},"de\u002Fformulas\u002Fmath\u002Fdiscrete-math\u002Frechnen-mit-kongruenzen","Rechnen mit Kongruenzen",{"stem":5097,"title":5098,"category":187},"de\u002Fformulas\u002Fmath\u002Fdiscrete-math\u002Fsatz-von-euler","Satz von Euler",1793824276559]