Pythagorean Triples

See Wikipedia: Pythagorean Triples

The Pythagorean Theorem says that if a and b are the lengths of the legs of a right trangle and c is the length of the hypotenuse, then a2 + b2 = c2.

Two legs of length 3 and 4 give us a hypotenuse of 5 — all whole numbers. When a, b and c are the legs and hypotenuse of a right trangle, and all three are whole numbers, we call that a "Pythagorean Triple". So we write the Pythagorean Triple "3, 4, 5" as "(3, 4, 5)".

The First 500 Pythagorean Triples (N, and the Pythagorean Triples of which N is an element):

NPythagorean Triples
3(3, 4, 5)
4(3, 4, 5)
5(3, 4, 5), (5, 12, 13)
7(7, 24, 25)
8(8, 15, 17)
9(9, 40, 41)
11(11, 60, 61)
12(5, 12, 13), (12, 35, 37)
13(5, 12, 13), (13, 84, 85)
15(8, 15, 17), (15, 112, 113)
16(16, 63, 65)
17(8, 15, 17), (17, 144, 145)
19(19, 180, 181)
20(20, 99, 101), (20, 21, 29)
21(21, 220, 221), (20, 21, 29)
23(23, 264, 265)
24(7, 24, 25), (24, 143, 145)
25(7, 24, 25), (25, 312, 313)
27(27, 364, 365)
28(28, 195, 197), (28, 45, 53)
29(29, 420, 421), (20, 21, 29)
31(31, 480, 481)
32(32, 255, 257)
33(33, 544, 545), (33, 56, 65)
35(12, 35, 37), (35, 612, 613)
36(36, 323, 325), (36, 77, 85)
37(12, 35, 37), (37, 684, 685)
39(39, 760, 761), (39, 80, 89)
40(9, 40, 41), (40, 399, 401)
41(9, 40, 41), (41, 840, 841)
43(43, 924, 925)
44(44, 483, 485), (44, 117, 125)
45(45, 1012, 1013), (28, 45, 53)
47(47, 1104, 1105)
48(48, 575, 577), (48, 55, 73)
49(49, 1200, 1201)
51(51, 140, 149), (51, 1300, 1301)
52(52, 675, 677), (52, 165, 173)
53(28, 45, 53), (53, 1404, 1405)
55(48, 55, 73), (55, 1512, 1513)
56(56, 783, 785), (33, 56, 65)
57(57, 176, 185), (57, 1624, 1625)
59(59, 1740, 1741)
60(11, 60, 61), (60, 899, 901), (60, 221, 229), (60, 91, 109)
61(11, 60, 61), (61, 1860, 1861)
63(16, 63, 65), (63, 1984, 1985)
64(64, 1023, 1025)
65(16, 63, 65), (33, 56, 65), (65, 72, 97), (65, 2112, 2113)
67(67, 2244, 2245)
68(68, 1155, 1157), (68, 285, 293)
69(69, 260, 269), (69, 2380, 2381)
71(71, 2520, 2521)
72(72, 1295, 1297), (65, 72, 97)
73(48, 55, 73), (73, 2664, 2665)
75(75, 308, 317), (75, 2812, 2813)
76(76, 1443, 1445), (76, 357, 365)
77(36, 77, 85), (77, 2964, 2965)
79(79, 3120, 3121)
80(80, 1599, 1601), (39, 80, 89)
81(81, 3280, 3281)
83(83, 3444, 3445)
84(13, 84, 85), (84, 1763, 1765), (84, 437, 445), (84, 187, 205)
85(13, 84, 85), (36, 77, 85), (85, 132, 157), (85, 3612, 3613)
87(87, 416, 425), (87, 3784, 3785)
88(88, 1935, 1937), (88, 105, 137)
89(39, 80, 89), (89, 3960, 3961)
91(60, 91, 109), (91, 4140, 4141)
92(92, 2115, 2117), (92, 525, 533)
93(93, 476, 485), (93, 4324, 4325)
95(95, 168, 193), (95, 4512, 4513)
96(96, 2303, 2305), (96, 247, 265)
97(65, 72, 97), (97, 4704, 4705)
99(20, 99, 101)
100(100, 621, 629)
101(20, 99, 101)
104(104, 153, 185)
105(105, 608, 617), (88, 105, 137), (105, 208, 233)
108(108, 725, 733)
109(60, 91, 109)
111(111, 680, 689)
112(15, 112, 113)
113(15, 112, 113)
115(115, 252, 277)
116(116, 837, 845)
117(44, 117, 125)
119(119, 120, 169)
120(120, 391, 409), (120, 209, 241), (119, 120, 169)
123(123, 836, 845)
124(124, 957, 965)
125(44, 117, 125)
129(129, 920, 929)
132(132, 1085, 1093), (132, 475, 493), (85, 132, 157)
133(133, 156, 205)
135(135, 352, 377)
136(136, 273, 305)
137(88, 105, 137)
140(140, 1221, 1229), (51, 140, 149), (140, 171, 221)
141(141, 1100, 1109)
143(24, 143, 145)
144(17, 144, 145)
145(24, 143, 145), (17, 144, 145), (145, 408, 433)
147(147, 1196, 1205)
148(148, 1365, 1373)
149(51, 140, 149)
152(152, 345, 377)
153(104, 153, 185)
155(155, 468, 493)
156(156, 1517, 1525), (156, 667, 685), (133, 156, 205)
157(85, 132, 157)
159(159, 1400, 1409)
160(160, 231, 281)
161(161, 240, 289)
164(164, 1677, 1685)
165(52, 165, 173), (165, 532, 557), (165, 1508, 1517)
168(168, 775, 793), (168, 425, 457), (95, 168, 193)
169(119, 120, 169)
171(140, 171, 221)
172(172, 1845, 1853)
173(52, 165, 173)
175(175, 288, 337)
176(57, 176, 185)
177(177, 1736, 1745)
180(19, 180, 181), (180, 2021, 2029), (180, 299, 349)
181(19, 180, 181)
183(183, 1856, 1865)
184(184, 513, 545)
185(57, 176, 185), (104, 153, 185), (185, 672, 697)
187(84, 187, 205)
188(188, 2205, 2213)
189(189, 340, 389)
192(192, 1015, 1033)
193(95, 168, 193)
195(28, 195, 197), (195, 748, 773), (195, 2108, 2117)
196(196, 2397, 2405)
197(28, 195, 197)
200(200, 609, 641)
201(201, 2240, 2249)
203(203, 396, 445)
204(204, 1147, 1165), (204, 253, 325)
205(84, 187, 205), (205, 828, 853), (133, 156, 205)
207(207, 224, 305)
208(105, 208, 233)
209(120, 209, 241)
213(213, 2516, 2525)
215(215, 912, 937)
216(216, 713, 745)
217(217, 456, 505)
219(219, 2660, 2669)
220(21, 220, 221), (220, 459, 509)
221(21, 220, 221), (60, 221, 229), (140, 171, 221)
224(207, 224, 305)
225(225, 272, 353)
228(228, 1435, 1453), (228, 325, 397)
229(60, 221, 229)
231(160, 231, 281), (231, 520, 569), (231, 2960, 2969)
232(232, 825, 857)
233(105, 208, 233)
235(235, 1092, 1117)
237(237, 3116, 3125)
240(240, 1591, 1609), (240, 551, 601), (161, 240, 289)
241(120, 209, 241)
245(245, 1188, 1213)
247(96, 247, 265)
248(248, 945, 977)
249(249, 3440, 3449)
252(115, 252, 277), (252, 275, 373)
253(204, 253, 325)
255(32, 255, 257), (255, 1288, 1313), (255, 3608, 3617)
257(32, 255, 257)
259(259, 660, 709)
260(69, 260, 269), (260, 651, 701)
261(261, 380, 461)
264(23, 264, 265), (264, 1927, 1945), (264, 1073, 1105)
265(23, 264, 265), (96, 247, 265), (265, 1392, 1417)
267(267, 3956, 3965)
269(69, 260, 269)
272(225, 272, 353)
273(136, 273, 305), (273, 736, 785), (273, 4136, 4145)
275(252, 275, 373)
276(276, 2107, 2125), (276, 493, 565)
277(115, 252, 277)
279(279, 440, 521)
280(280, 1209, 1241), (280, 759, 809), (280, 351, 449)
281(160, 231, 281)
285(68, 285, 293), (285, 1612, 1637), (285, 4508, 4517)
287(287, 816, 865)
288(175, 288, 337)
289(161, 240, 289)
293(68, 285, 293)
295(295, 1728, 1753)
296(296, 1353, 1385)
297(297, 304, 425)
299(180, 299, 349)
300(300, 589, 661)
301(301, 900, 949)
304(297, 304, 425)
305(136, 273, 305), (207, 224, 305), (305, 1848, 1873)
308(75, 308, 317), (308, 435, 533)
312(25, 312, 313), (312, 1505, 1537)
313(25, 312, 313)
315(315, 988, 1037), (315, 572, 653), (315, 1972, 1997)
317(75, 308, 317)
319(319, 360, 481)
320(320, 999, 1049)
323(36, 323, 325)
325(36, 323, 325), (204, 253, 325), (228, 325, 397)
328(328, 1665, 1697)
329(329, 1080, 1129)
333(333, 644, 725)
335(335, 2232, 2257)
336(336, 527, 625), (336, 377, 505)
337(175, 288, 337)
340(340, 1131, 1181), (189, 340, 389)
341(341, 420, 541)
344(344, 1833, 1865)
345(152, 345, 377), (345, 2368, 2393)
348(348, 805, 877)
349(180, 299, 349)
351(280, 351, 449)
352(135, 352, 377)
353(225, 272, 353)
355(355, 2508, 2533)
357(76, 357, 365), (357, 1276, 1325)
360(360, 2009, 2041), (360, 1271, 1321), (319, 360, 481)
364(27, 364, 365), (364, 627, 725)
365(27, 364, 365), (76, 357, 365), (365, 2652, 2677)
368(368, 465, 593)
369(369, 800, 881)
371(371, 1380, 1429)
372(372, 925, 997)
373(252, 275, 373)
376(376, 2193, 2225)
377(152, 345, 377), (135, 352, 377), (336, 377, 505)
380(380, 1419, 1469), (261, 380, 461)
385(385, 552, 673), (385, 1488, 1537), (385, 2952, 2977)
387(387, 884, 965)
389(189, 340, 389)
391(120, 391, 409)
392(392, 2385, 2417)
395(395, 3108, 3133)
396(203, 396, 445), (396, 403, 565)
397(228, 325, 397)
399(40, 399, 401), (399, 1600, 1649)
400(400, 561, 689)
401(40, 399, 401)
403(396, 403, 565)
405(405, 3268, 3293)
407(407, 624, 745)
408(145, 408, 433)
409(120, 391, 409)
413(413, 1716, 1765)
415(415, 3432, 3457)
416(87, 416, 425)
420(29, 420, 421), (420, 1739, 1789), (420, 1189, 1261), (420, 851, 949), (341, 420, 541)
421(29, 420, 421)
423(423, 1064, 1145)
425(87, 416, 425), (168, 425, 457), (297, 304, 425)
427(427, 1836, 1885)
429(429, 460, 629), (429, 700, 821)
432(432, 665, 793)
433(145, 408, 433)
435(308, 435, 533), (435, 3772, 3797)
437(84, 437, 445)
440(440, 1911, 1961), (279, 440, 521)
441(441, 1160, 1241)
444(444, 1333, 1405)
445(84, 437, 445), (203, 396, 445), (445, 3948, 3973)
448(448, 975, 1073)
449(280, 351, 449)
451(451, 780, 901)
455(455, 528, 697), (455, 2088, 2137), (455, 4128, 4153)
456(217, 456, 505)
457(168, 425, 457)
459(220, 459, 509)
460(460, 2091, 2141), (429, 460, 629)
461(261, 380, 461)
464(464, 777, 905)
465(368, 465, 593), (465, 4312, 4337)
468(155, 468, 493), (468, 595, 757)
469(469, 2220, 2269)
473(473, 864, 985)
475(132, 475, 493)
476(93, 476, 485), (476, 1107, 1205)
477(477, 1364, 1445)
480(31, 480, 481), (480, 2279, 2329)
481(31, 480, 481), (319, 360, 481), (481, 600, 769)
483(44, 483, 485), (483, 2356, 2405)
485(44, 483, 485), (93, 476, 485)
492(492, 1645, 1717)
493(132, 475, 493), (155, 468, 493), (276, 493, 565)
495(495, 952, 1073), (495, 1472, 1553)
496(496, 897, 1025)
497(497, 2496, 2545)
504(504, 1247, 1345), (504, 703, 865)
505(217, 456, 505), (336, 377, 505)
509(220, 459, 509)
511(511, 2640, 2689)
513(184, 513, 545)
516(516, 1813, 1885)
517(517, 1044, 1165)
520(231, 520, 569)
521(279, 440, 521)
525(92, 525, 533), (525, 2788, 2837)
527(336, 527, 625)
528(528, 1025, 1153), (455, 528, 697)
531(531, 1700, 1781)
532(165, 532, 557), (532, 1395, 1493)
533(92, 525, 533), (308, 435, 533), (533, 756, 925)
539(539, 1140, 1261)
540(540, 629, 829)
541(341, 420, 541)
544(33, 544, 545)
545(33, 544, 545), (184, 513, 545)
549(549, 1820, 1901)
551(240, 551, 601)
552(385, 552, 673)
553(553, 3096, 3145)
555(555, 572, 797)
557(165, 532, 557)
559(559, 840, 1009)
560(560, 1551, 1649), (560, 1161, 1289)
561(400, 561, 689), (561, 1240, 1361)
564(564, 2173, 2245)
565(276, 493, 565), (396, 403, 565)
567(567, 3256, 3305)
569(231, 520, 569)
572(315, 572, 653), (555, 572, 797)
575(48, 575, 577)
576(576, 943, 1105)
577(48, 575, 577)
580(580, 741, 941)
581(581, 3420, 3469)
583(583, 1344, 1465)
585(585, 928, 1097), (585, 2072, 2153)
588(588, 2365, 2437)
589(300, 589, 661)
592(592, 1305, 1433)
593(368, 465, 593)
595(468, 595, 757), (595, 3588, 3637)
600(481, 600, 769)
601(240, 551, 601)
603(603, 2204, 2285)
608(105, 608, 617)
609(200, 609, 641), (609, 3760, 3809)
611(611, 1020, 1189)
612(35, 612, 613), (612, 1075, 1237)
613(35, 612, 613)
615(615, 728, 953)
616(616, 1887, 1985), (616, 663, 905)
617(105, 608, 617)
620(620, 861, 1061)
621(100, 621, 629)
623(623, 3936, 3985)
624(624, 1457, 1585), (407, 624, 745)
625(336, 527, 625)
627(364, 627, 725), (627, 1564, 1685)
629(100, 621, 629), (429, 460, 629), (540, 629, 829)
637(637, 1116, 1285)
639(639, 2480, 2561)
641(200, 609, 641)
644(644, 2067, 2165), (333, 644, 725)
645(645, 812, 1037)
649(649, 1680, 1801)
651(260, 651, 701)
653(315, 572, 653)
656(656, 1617, 1745)
657(657, 2624, 2705)
660(259, 660, 709), (660, 989, 1189), (660, 779, 1021)
661(300, 589, 661)
663(616, 663, 905), (663, 1216, 1385)
665(432, 665, 793)
667(156, 667, 685)
671(671, 1800, 1921)
672(185, 672, 697), (672, 2255, 2353)
673(385, 552, 673)
675(52, 675, 677)
677(52, 675, 677)
680(111, 680, 689)
684(37, 684, 685), (684, 1363, 1525)
685(37, 684, 685), (156, 667, 685)
688(688, 1785, 1913)
689(111, 680, 689), (400, 561, 689), (689, 1320, 1489)
693(693, 1924, 2045), (693, 2924, 3005)
696(696, 697, 985)
697(185, 672, 697), (455, 528, 697), (696, 697, 985)
700(429, 700, 821)
701(260, 651, 701)
703(504, 703, 865)
704(704, 903, 1145)
705(705, 992, 1217)
709(259, 660, 709)
711(711, 3080, 3161)
713(216, 713, 745)
715(715, 1428, 1597), (715, 2052, 2173)
720(720, 1961, 2089), (720, 1519, 1681)
725(108, 725, 733), (364, 627, 725), (333, 644, 725)
728(615, 728, 953)
731(731, 780, 1069)
733(108, 725, 733)
735(735, 1088, 1313)
736(273, 736, 785)
737(737, 2184, 2305)
740(740, 1269, 1469)
741(580, 741, 941), (741, 1540, 1709)
744(744, 817, 1105)
745(216, 713, 745), (407, 624, 745)
747(747, 3404, 3485)
748(195, 748, 773), (748, 1035, 1277)
752(752, 2145, 2273)
756(533, 756, 925)
757(468, 595, 757)
759(280, 759, 809), (759, 2320, 2441)
760(39, 760, 761)
761(39, 760, 761)
765(765, 868, 1157), (765, 3572, 3653)
767(767, 1656, 1825)
769(481, 600, 769)
773(195, 748, 773)
775(168, 775, 793)
777(464, 777, 905)
779(660, 779, 1021)
780(780, 1421, 1621), (451, 780, 901), (731, 780, 1069)
781(781, 2460, 2581)
783(56, 783, 785)
784(784, 2337, 2465)
785(56, 783, 785), (273, 736, 785)
792(792, 1855, 2017), (792, 1175, 1417)
793(168, 775, 793), (432, 665, 793), (793, 1776, 1945)
795(795, 1292, 1517)
797(555, 572, 797)
799(799, 960, 1249)
800(369, 800, 881)
801(801, 3920, 4001)
803(803, 2604, 2725)
805(348, 805, 877)
809(280, 759, 809)
812(645, 812, 1037)
816(287, 816, 865)
817(744, 817, 1105)
819(819, 1900, 2069)
820(820, 1581, 1781)
821(429, 700, 821)
825(232, 825, 857), (825, 2752, 2873)
828(205, 828, 853), (828, 2035, 2197)
829(540, 629, 829)
832(832, 855, 1193)
833(833, 1056, 1345)
836(123, 836, 845), (836, 1323, 1565)
837(116, 837, 845)
840(41, 840, 841), (840, 1081, 1369), (559, 840, 1009)
841(41, 840, 841)
845(116, 837, 845), (123, 836, 845)
851(420, 851, 949)
853(205, 828, 853)
855(832, 855, 1193)
857(232, 825, 857)
860(860, 1749, 1949)
861(620, 861, 1061)
864(473, 864, 985)
865(287, 816, 865), (504, 703, 865)
868(765, 868, 1157)
869(869, 3060, 3181)
871(871, 2160, 2329)
877(348, 805, 877)
880(880, 1479, 1721)
881(369, 800, 881)
884(387, 884, 965), (884, 987, 1325)
885(885, 1628, 1853)
888(888, 1225, 1513)
891(891, 3220, 3341)
893(893, 924, 1285)
897(496, 897, 1025), (897, 2296, 2465)
899(60, 899, 901)
900(301, 900, 949)
901(60, 899, 901), (451, 780, 901), (901, 1260, 1549)
903(704, 903, 1145)
905(464, 777, 905), (616, 663, 905)
912(215, 912, 937)
913(913, 3384, 3505)
915(915, 1748, 1973)
920(129, 920, 929)
923(923, 2436, 2605)
924(43, 924, 925), (924, 1643, 1885), (893, 924, 1285)
925(43, 924, 925), (372, 925, 997), (533, 756, 925)
928(585, 928, 1097)
929(129, 920, 929)
931(931, 1020, 1381)
935(935, 1368, 1657), (935, 3552, 3673)
936(936, 1127, 1465)
937(215, 912, 937)
940(940, 2109, 2309)
941(580, 741, 941)
943(576, 943, 1105)
945(248, 945, 977)
949(420, 851, 949), (301, 900, 949), (949, 2580, 2749)
952(495, 952, 1073)
953(615, 728, 953)
957(124, 957, 965), (957, 3724, 3845)
960(799, 960, 1249)
965(124, 957, 965), (387, 884, 965)
969(969, 1120, 1481), (969, 1480, 1769)
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