43:
and many of its open problems are easily understood even by non-mathematicians. More generally, the field has come to be concerned with a wider class of problems that arise naturally from the study of integers. Number theory may be subdivided into several fields according to the methods used and the
935:
1938:
776:
770:
1270:
729:
1661:
826:
1496:
967:
1213:
1854:
1491:
1362:
1255:
987:
357:
1773:
1312:
398:
208:
57:
1579:
705:
591:
439:
1424:
895:
269:
1827:
1193:
611:
286:
1958:
1879:
1656:
1646:
1337:
1295:
1203:
415:
1953:
1265:
316:
1864:
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749:
459:
374:
333:
299:
45:
1708:
1223:
860:
1889:
1790:
1763:
1609:
1599:
1136:
1049:
920:
915:
557:
479:
1584:
1439:
1384:
1290:
1332:
1300:
1131:
1126:
516:
496:
1899:
1812:
1486:
1429:
1342:
885:
831:
232:
1671:
1614:
1523:
1233:
1228:
905:
685:
644:
1641:
1419:
1054:
972:
1723:
1604:
1394:
1379:
1198:
865:
631:
533:
252:
66:
1914:
1501:
1151:
992:
661:
574:
1859:
1589:
1832:
1795:
1698:
1557:
1444:
1434:
1317:
1260:
1094:
1034:
1029:
1012:
962:
880:
1738:
1459:
1449:
1357:
178:
175:
172:
169:
166:
163:
160:
157:
154:
151:
148:
145:
142:
139:
136:
133:
130:
127:
124:
121:
118:
115:
112:
109:
106:
103:
98:
1651:
1208:
1044:
8:
1929:
1785:
1693:
1676:
1481:
900:
1904:
1807:
1753:
1414:
1079:
930:
925:
52:
1768:
1374:
1178:
1074:
947:
843:
726:
1322:
1817:
1352:
1146:
1111:
1059:
957:
890:
500:
84:
1540:
1389:
753:
665:
273:
236:
212:
1909:
1748:
1688:
1626:
1535:
1506:
1409:
1399:
1250:
1166:
1039:
982:
910:
875:
870:
814:
709:
689:
648:
635:
578:
520:
483:
463:
419:
361:
337:
320:
303:
290:
256:
17:
733:
615:
74:
1884:
1837:
1733:
1631:
1594:
1562:
1545:
1518:
1245:
1218:
1156:
1069:
1024:
855:
595:
561:
537:
443:
402:
378:
1636:
769:
The following 200 pages are in this category, out of approximately 217 total.
354:
1947:
1924:
1874:
1849:
1728:
1718:
1703:
1666:
1471:
1404:
1183:
1161:
1084:
1007:
997:
977:
952:
792:
31:
22:
395:
205:
1919:
1869:
1567:
1476:
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1106:
1064:
809:
588:
436:
266:
1894:
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1713:
283:
36:
412:
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1454:
1327:
1285:
1280:
1002:
804:
313:
70:
371:
330:
1822:
1116:
554:
493:
229:
193:
This category has the following 29 subcategories, out of 29 total.
682:
530:
40:
658:
571:
93:
78:
936:
AWM–Microsoft
Research Prize in Algebra and Number Theory
1945:
86:
44:questions investigated. See for example the
1271:Formulas for generating Pythagorean triples
1662:Noncommutative unique factorization domain
827:List of recreational number theory topics
1497:An Introduction to the Theory of Numbers
968:Bernoulli polynomials of the second kind
771:This list may not reflect recent changes
1946:
1256:Proofs of Fermat's little theorem
988:Birch and Swinnerton-Dyer conjecture
188:
13:
1492:Inter-universal TeichmĂĽller theory
780:
730:Unsolved problems in number theory
195:
187:
14:
1970:
1580:Minimal polynomial of 2cos(2pi/n)
766:Pages in category "Number theory"
39:concerned with the properties of
1425:History of the Theory of Numbers
896:Arithmetic hyperbolic 3-manifold
1828:Residue-class-wise affine group
1880:Short integer solution problem
1657:Non-integer base of numeration
1647:New York Number Theory Seminar
1363:Grothendieck–Teichmüller group
1296:List of mathematical functions
1204:Elliptic divisibility sequence
1:
1855:Schoof–Elkies–Atkin algorithm
1224:Euler's totient function
1214:Erdős–Tenenbaum–Ford constant
861:Abel's summation formula
1585:Mirimanoff's congruence
1440:Hooley's delta function
1385:Haran's diamond theorem
1142:Distribution (number theory)
1090:Cyclic number (group theory)
788:List of number theory topics
764:
46:list of number theory topics
7:
1890:Signed-digit representation
1791:Quadratic irrational number
1774:Prouhet–Thue–Morse constant
1764:Probabilistic number theory
1610:Multiplicative independence
1600:Multiplicative digital root
1313:Gan–Gross–Prasad conjecture
1194:Eisenstein–Kronecker number
1137:Disquisitiones Arithmeticae
1050:Computational number theory
921:Aurifeuillean factorization
358:Computational number theory
10:
1975:
1338:Glaisher–Kinkelin constant
1333:Generalized taxicab number
1301:List of types of functions
1132:Dirichlet series inversion
1127:Dirichlet hyperbola method
16:The main article for this
15:
1900:Skew binary number system
1813:Random Fibonacci sequence
1709:P-adic TeichmĂĽller theory
1487:Integer-valued polynomial
1420:Hilbert's inequality
1343:Glossary of number theory
1266:Fontaine–Mazur conjecture
973:Bertrand's postulate
886:Arithmetic Fuchsian group
832:Timeline of number theory
399:Diophantine approximation
209:Theorems in number theory
1865:Schwartz–Bruhat function
1672:Number Theory Foundation
1615:Multiplicative partition
1524:Journal of Number Theory
1234:Extended natural numbers
1229:Eventually (mathematics)
906:Arithmetic zeta function
706:Squares in number theory
592:Multiplicative functions
440:Elementary number theory
1860:Schoof's algorithm
1724:Persistence of a number
1605:Multiplicative function
1590:Moessner's theorem
1395:Harmonic divisor number
1199:Elkies trinomial curves
916:Artin–Hasse exponential
866:Algebraic number theory
270:Algebraic number theory
55:corresponds roughly to
1915:Solenoid (mathematics)
1502:Irrationality sequence
1152:Divisor sum identities
612:Number theory journals
287:Analytic number theory
1959:Fields of mathematics
1833:Ring of modular forms
1796:Quadratic reciprocity
1699:P-adic gamma function
1652:Niven's constant
1558:Least common multiple
1445:Hundred Fowls Problem
1430:Hodge–Arakelov theory
1318:Gauss composition law
1261:Fifth power (algebra)
1095:Cyclotomic polynomial
1055:Contou-Carrère symbol
1045:Cobham's theorem
1035:Change-making problem
1030:Champernowne constant
963:Bernoulli polynomials
881:Arithmetic derivative
416:Diophantine equations
1954:Discrete mathematics
1905:Skewes's number
1808:Ramanujan's sum
1739:Prime omega function
1460:Hyperharmonic number
1450:Hurwitz class number
1358:Gregory coefficients
1291:Fueter–Pólya theorem
1013:BĂĽchi's problem
317:Arithmetic functions
1930:Square-free integer
1786:Q-Pochhammer symbol
1694:P-adic distribution
1677:Numerical semigroup
1482:Integer square root
1380:Hall–Higman theorem
901:Arithmetic topology
750:Number theory stubs
460:Geometry of numbers
375:Continued fractions
334:Arithmetic geometry
300:Arithmetic dynamics
1754:Primefree sequence
1415:Maria Heep-Altiner
1323:Gauss's diary
1080:Cunningham Project
993:Bost–Connes system
931:Auxiliary function
926:Automorphic number
558:Modular arithmetic
480:Integer partitions
1937:(previous page) (
1769:Prosolvable group
1642:Néron–Tate height
1435:Hodge–Tate module
1375:Half-period ratio
1209:Erdős arcsine law
1179:Egyptian fraction
1075:Cunningham number
948:Barnes G-function
775:(previous page) (
517:Langlands program
497:Integer sequences
35:is the branch of
1966:
1818:Redheffer matrix
1353:Granville number
1147:Divisor function
1112:Deformation ring
1060:Coprime integers
958:Bernoulli number
891:Arithmetic group
844:3x + 1 semigroup
755:
735:
728:
711:
691:
684:
667:
660:
650:
637:
617:
597:
590:
580:
573:
563:
556:
539:
532:
522:
502:
495:
485:
465:
445:
438:
421:
414:
404:
397:
380:
373:
363:
356:
339:
332:
322:
315:
305:
292:
285:
275:
268:
258:
238:
233:Number theorists
231:
214:
207:
1974:
1973:
1969:
1968:
1967:
1965:
1964:
1963:
1944:
1943:
1942:
1936:
1935:
1934:
1910:Sociable number
1842:
1800:
1778:
1749:Prime signature
1689:P-adic analysis
1681:
1627:Natural density
1619:
1572:
1550:
1536:Kaprekar number
1528:
1511:
1507:Iwasawa algebra
1464:
1410:Hecke character
1400:Harmonic number
1367:
1305:
1251:Fermat quotient
1238:
1171:
1167:Dyadic rational
1099:
1040:Character group
1017:
983:Binomial number
940:
911:Artin conductor
876:Amicable triple
871:Amenable number
848:
836:
819:
815:Ribenboim Prize
797:
763:
762:
761:
760:
757:
756:
740:
737:
736:
725:
716:
713:
712:
696:
693:
692:
686:Quadratic forms
681:
672:
669:
668:
657:
652:
651:
645:Perfect numbers
639:
638:
622:
619:
618:
602:
599:
598:
587:
582:
581:
570:
565:
564:
553:
544:
541:
540:
529:
524:
523:
507:
504:
503:
492:
487:
486:
470:
467:
466:
450:
447:
446:
435:
426:
423:
422:
411:
406:
405:
394:
385:
382:
381:
370:
365:
364:
353:
344:
341:
340:
329:
324:
323:
312:
307:
306:
294:
293:
282:
277:
276:
265:
260:
259:
243:
240:
239:
228:
219:
216:
215:
204:
186:
185:
184:
183:
89:
29:Traditionally,
27:
12:
11:
5:
1972:
1962:
1961:
1956:
1933:
1932:
1927:
1922:
1917:
1912:
1907:
1902:
1897:
1892:
1887:
1885:Sidon sequence
1882:
1877:
1872:
1867:
1862:
1857:
1852:
1846:
1843:
1841:
1840:
1838:Ruler function
1835:
1830:
1825:
1820:
1815:
1810:
1804:
1801:
1799:
1798:
1793:
1788:
1782:
1779:
1777:
1776:
1771:
1766:
1761:
1756:
1751:
1746:
1741:
1736:
1734:Prime geodesic
1731:
1726:
1721:
1716:
1711:
1706:
1701:
1696:
1691:
1685:
1682:
1680:
1679:
1674:
1669:
1664:
1659:
1654:
1649:
1644:
1639:
1634:
1632:Natural number
1629:
1623:
1620:
1618:
1617:
1612:
1607:
1602:
1597:
1595:Multipartition
1592:
1587:
1582:
1576:
1573:
1571:
1570:
1565:
1563:Local analysis
1560:
1554:
1551:
1549:
1548:
1546:Kubilius model
1543:
1538:
1532:
1529:
1527:
1526:
1521:
1519:Jacobsthal sum
1515:
1512:
1510:
1509:
1504:
1499:
1494:
1489:
1484:
1479:
1474:
1468:
1465:
1463:
1462:
1457:
1452:
1447:
1442:
1437:
1432:
1427:
1422:
1417:
1412:
1407:
1402:
1397:
1392:
1387:
1382:
1377:
1371:
1368:
1366:
1365:
1360:
1355:
1350:
1345:
1340:
1335:
1330:
1325:
1320:
1315:
1309:
1306:
1304:
1303:
1298:
1293:
1288:
1283:
1278:
1273:
1268:
1263:
1258:
1253:
1248:
1246:Farey sequence
1242:
1239:
1237:
1236:
1231:
1226:
1221:
1219:Euler function
1216:
1211:
1206:
1201:
1196:
1191:
1186:
1181:
1175:
1172:
1170:
1169:
1164:
1159:
1157:Ducci sequence
1154:
1149:
1144:
1139:
1134:
1129:
1124:
1119:
1114:
1109:
1103:
1100:
1098:
1097:
1092:
1087:
1082:
1077:
1072:
1070:Cube (algebra)
1067:
1062:
1057:
1052:
1047:
1042:
1037:
1032:
1027:
1025:Cabtaxi number
1021:
1018:
1016:
1015:
1010:
1005:
1000:
995:
990:
985:
980:
975:
970:
965:
960:
955:
950:
944:
941:
939:
938:
933:
928:
923:
918:
913:
908:
903:
898:
893:
888:
883:
878:
873:
868:
863:
858:
856:Abc conjecture
852:
849:
847:
846:
840:
837:
835:
834:
829:
823:
820:
818:
817:
812:
807:
801:
798:
796:
795:
790:
784:
782:
781:
767:
759:
758:
748:
747:
744:
741:
739:
738:
724:
723:
720:
717:
715:
714:
704:
703:
700:
697:
695:
694:
680:
679:
676:
673:
671:
670:
656:
655:
653:
643:
642:
640:
632:P-adic numbers
630:
629:
626:
623:
621:
620:
610:
609:
606:
603:
601:
600:
586:
585:
583:
569:
568:
566:
552:
551:
548:
545:
543:
542:
534:Lattice points
528:
527:
525:
515:
514:
511:
508:
506:
505:
491:
490:
488:
478:
477:
474:
471:
469:
468:
458:
457:
454:
451:
449:
448:
434:
433:
430:
427:
425:
424:
410:
409:
407:
393:
392:
389:
386:
384:
383:
369:
368:
366:
352:
351:
348:
345:
343:
342:
328:
327:
325:
311:
310:
308:
298:
297:
295:
281:
280:
278:
264:
263:
261:
253:Abc conjecture
251:
250:
247:
244:
242:
241:
227:
226:
223:
220:
218:
217:
203:
202:
199:
197:
196:
191:
182:
181:
101:
96:
90:
88:
85:
83:
9:
6:
4:
3:
2:
1971:
1960:
1957:
1955:
1952:
1951:
1949:
1940:
1931:
1928:
1926:
1925:Square number
1923:
1921:
1918:
1916:
1913:
1911:
1908:
1906:
1903:
1901:
1898:
1896:
1893:
1891:
1888:
1886:
1883:
1881:
1878:
1876:
1875:Seventh power
1873:
1871:
1868:
1866:
1863:
1861:
1858:
1856:
1853:
1851:
1850:Schnorr group
1848:
1847:
1844:
1839:
1836:
1834:
1831:
1829:
1826:
1824:
1821:
1819:
1816:
1814:
1811:
1809:
1806:
1805:
1802:
1797:
1794:
1792:
1789:
1787:
1784:
1783:
1780:
1775:
1772:
1770:
1767:
1765:
1762:
1760:
1757:
1755:
1752:
1750:
1747:
1745:
1742:
1740:
1737:
1735:
1732:
1730:
1729:Poussin proof
1727:
1725:
1722:
1720:
1719:Perfect power
1717:
1715:
1712:
1710:
1707:
1705:
1704:P-adic number
1702:
1700:
1697:
1695:
1692:
1690:
1687:
1686:
1683:
1678:
1675:
1673:
1670:
1668:
1667:Normal number
1665:
1663:
1660:
1658:
1655:
1653:
1650:
1648:
1645:
1643:
1640:
1638:
1635:
1633:
1630:
1628:
1625:
1624:
1621:
1616:
1613:
1611:
1608:
1606:
1603:
1601:
1598:
1596:
1593:
1591:
1588:
1586:
1583:
1581:
1578:
1577:
1574:
1569:
1566:
1564:
1561:
1559:
1556:
1555:
1552:
1547:
1544:
1542:
1541:Knödel number
1539:
1537:
1534:
1533:
1530:
1525:
1522:
1520:
1517:
1516:
1513:
1508:
1505:
1503:
1500:
1498:
1495:
1493:
1490:
1488:
1485:
1483:
1480:
1478:
1475:
1473:
1472:Ideal lattice
1470:
1469:
1466:
1461:
1458:
1456:
1453:
1451:
1448:
1446:
1443:
1441:
1438:
1436:
1433:
1431:
1428:
1426:
1423:
1421:
1418:
1416:
1413:
1411:
1408:
1406:
1405:Hecke algebra
1403:
1401:
1398:
1396:
1393:
1391:
1390:GĂĽnter Harder
1388:
1386:
1383:
1381:
1378:
1376:
1373:
1372:
1369:
1364:
1361:
1359:
1356:
1354:
1351:
1349:
1346:
1344:
1341:
1339:
1336:
1334:
1331:
1329:
1326:
1324:
1321:
1319:
1316:
1314:
1311:
1310:
1307:
1302:
1299:
1297:
1294:
1292:
1289:
1287:
1284:
1282:
1279:
1277:
1274:
1272:
1269:
1267:
1264:
1262:
1259:
1257:
1254:
1252:
1249:
1247:
1244:
1243:
1240:
1235:
1232:
1230:
1227:
1225:
1222:
1220:
1217:
1215:
1212:
1210:
1207:
1205:
1202:
1200:
1197:
1195:
1192:
1190:
1187:
1185:
1184:Eichler order
1182:
1180:
1177:
1176:
1173:
1168:
1165:
1163:
1162:Durfee square
1160:
1158:
1155:
1153:
1150:
1148:
1145:
1143:
1140:
1138:
1135:
1133:
1130:
1128:
1125:
1123:
1120:
1118:
1115:
1113:
1110:
1108:
1105:
1104:
1101:
1096:
1093:
1091:
1088:
1086:
1085:Cyclic number
1083:
1081:
1078:
1076:
1073:
1071:
1068:
1066:
1063:
1061:
1058:
1056:
1053:
1051:
1048:
1046:
1043:
1041:
1038:
1036:
1033:
1031:
1028:
1026:
1023:
1022:
1019:
1014:
1011:
1009:
1008:Brjuno number
1006:
1004:
1001:
999:
998:Brandt matrix
996:
994:
991:
989:
986:
984:
981:
979:
978:Bhargava cube
976:
974:
971:
969:
966:
964:
961:
959:
956:
954:
953:Basel problem
951:
949:
946:
945:
942:
937:
934:
932:
929:
927:
924:
922:
919:
917:
914:
912:
909:
907:
904:
902:
899:
897:
894:
892:
889:
887:
884:
882:
879:
877:
874:
872:
869:
867:
864:
862:
859:
857:
854:
853:
850:
845:
842:
841:
838:
833:
830:
828:
825:
824:
821:
816:
813:
811:
808:
806:
803:
802:
799:
794:
793:Number theory
791:
789:
786:
785:
783:
778:
774:
772:
765:
751:
746:
745:
742:
731:
727:
722:
721:
718:
707:
702:
701:
698:
687:
683:
678:
677:
674:
663:
662:Prime numbers
659:
654:
646:
641:
633:
628:
627:
624:
613:
608:
607:
604:
593:
589:
584:
576:
575:Modular forms
572:
567:
559:
555:
550:
549:
546:
535:
531:
526:
518:
513:
512:
509:
501:(10 C, 220 P)
498:
494:
489:
481:
476:
475:
472:
461:
456:
455:
452:
441:
437:
432:
431:
428:
417:
413:
408:
400:
396:
391:
390:
387:
376:
372:
367:
359:
355:
350:
349:
346:
335:
331:
326:
318:
314:
309:
301:
296:
288:
284:
279:
271:
267:
262:
254:
249:
248:
245:
234:
230:
225:
224:
221:
210:
206:
201:
200:
198:
194:
190:Subcategories
189:
180:
177:
174:
171:
168:
165:
162:
159:
156:
153:
150:
147:
144:
141:
138:
135:
132:
129:
126:
123:
120:
117:
114:
111:
108:
105:
102:
100:
97:
95:
92:
91:
82:
80:
76:
72:
68:
64:
63:Number theory
61:
59:
54:
49:
47:
42:
38:
34:
33:
32:number theory
25:
24:
23:Number theory
19:
1920:Sparse ruler
1870:Selmer group
1568:Lone divider
1477:Ideal number
1348:Golomb ruler
1276:Fourth power
1189:Eighth power
1122:Digital root
1107:Dedekind sum
1065:Covering set
810:Fermat Prize
768:
734:(1 C, 106 P)
666:(12 C, 60 P)
274:(7 C, 129 P)
237:(6 C, 229 P)
213:(5 C, 106 P)
192:
62:
56:
50:
30:
28:
21:
1895:Sixth power
1744:Prime power
1714:Paley graph
1637:NĂ©ron model
690:(2 C, 61 P)
596:(1 C, 13 P)
579:(3 C, 79 P)
562:(1 C, 62 P)
538:(1 C, 39 P)
444:(1 C, 12 P)
420:(4 C, 64 P)
403:(1 C, 35 P)
379:(1 C, 30 P)
362:(2 C, 17 P)
338:(3 C, 11 P)
321:(4 C, 29 P)
291:(7 C, 74 P)
37:mathematics
1948:Categories
1759:Primon gas
1455:Hydra game
1328:GCD matrix
1286:Frobenioid
1281:Frey curve
1003:Brewer sum
805:Cole Prize
71:MathSciNet
1939:next page
1823:Remainder
1117:Digit sum
777:next page
87:Contents
53:category
41:integers
18:category
754:(120 P)
710:(37 P)
649:(11 P)
636:(18 P)
521:(20 P)
484:(15 P)
464:(12 P)
304:(37 P)
257:(29 P)
79:zbMATH
65:; see
616:(6 P)
75:11-XX
73:and
67:11-XX
60:11-XX
51:This
839:0–9
99:0–9
94:Top
77:at
69:at
58:MSC
20:is
1950::
1941:)
773:.
752:‎
732:‎
708:‎
688:‎
664:‎
647:‎
634:‎
614:‎
594:‎
577:‎
560:‎
536:‎
519:‎
499:‎
482:‎
462:‎
442:‎
418:‎
401:‎
377:‎
360:‎
336:‎
319:‎
302:‎
289:‎
272:‎
255:‎
235:‎
211:‎
81:.
48:.
1845:S
1803:R
1781:Q
1684:P
1622:N
1575:M
1553:L
1531:K
1514:J
1467:I
1370:H
1308:G
1241:F
1174:E
1102:D
1020:C
943:B
851:A
822:*
800:.
779:)
743:ÎŁ
719:U
699:S
675:Q
625:P
605:N
547:M
510:L
473:I
453:G
429:E
388:D
347:C
246:A
222:*
179:Z
176:Y
173:X
170:W
167:V
164:U
161:T
158:S
155:R
152:Q
149:P
146:O
143:N
140:M
137:L
134:K
131:J
128:I
125:H
122:G
119:F
116:E
113:D
110:C
107:B
104:A
26:.
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