A Pythagorean Triple is a triple of natural numbers (a,b,c) such that
It's easy to see that if x > y > 0 are natural numbers then
A Pythagorean Triple is primitive if the greatest common factor of a,b,c is 1. For example, (3,4,5) is primitive and (6,8,10) is not. Following is a list of all primitive Pythagorean triples where a, b, c are all less than 1000.
(3,4,5), (5,12,13), (7,24,25), (8,15,17), (9,40,41), (11,60,61), (12,35,37), (13,84,85), (15,112,113), (16,63,65), (17,144,145), (19,180,181), (20,21,29), (20,99,101), (21,220,221), (23,264,265), (24,143,145), (25,312,313), (27,364,365), (28,45,53), (28,195,197), (29,420,421), (31,480,481), (32,255,257), (33,56,65), (33,544,545), (35,612,613), (36,77,85), (36,323,325), (37,684,685), (39,80,89), (39,760,761), (40,399,401), (41,840,841), (43,924,925), (44,117,125), (44,483,485), (48,55,73), (48,575,577), (51,140,149), (52,165,173), (52,675,677), (56,783,785), (57,176,185), (60,91,109), (60,221,229), (60,899,901), (65,72,97), (68,285,293), (69,260,269), (75,308,317), (76,357,365), (84,187,205), (84,437,445), (85,132,157), (87,416,425), (88,105,137), (92,525,533), (93,476,485), (95,168,193), (96,247,265), (100,621,629), (104,153,185), (105,208,233), (105,608,617), (108,725,733), (111,680,689), (115,252,277), (116,837,845), (119,120,169), (120,209,241), (120,391,409), (123,836,845), (124,957,965), (129,920,929), (132,475,493), (133,156,205), (135,352,377), (136,273,305), (140,171,221), (145,408,433), (152,345,377), (155,468,493), (156,667,685), (160,231,281), (161,240,289), (165,532,557), (168,425,457), (168,775,793), (175,288,337), (180,299,349), (184,513,545), (185,672,697), (189,340,389), (195,748,773), (200,609,641), (203,396,445), (204,253,325), (205,828,853), (207,224,305), (215,912,937), (216,713,745), (217,456,505), (220,459,509), (225,272,353), (228,325,397), (231,520,569), (232,825,857), (240,551,601), (248,945,977), (252,275,373), (259,660,709), (260,651,701), (261,380,461), (273,736,785), (276,493,565), (279,440,521), (280,351,449), (280,759,809), (287,816,865), (297,304,425), (300,589,661), (301,900,949), (308,435,533), (315,572,653), (319,360,481), (333,644,725), (336,377,505), (336,527,625), (341,420,541), (348,805,877), (364,627,725), (368,465,593), (369,800,881), (372,925,997), (385,552,673), (387,884,965), (396,403,565), (400,561,689), (407,624,745), (420,851,949), (429,460,629), (429,700,821), (432,665,793), (451,780,901), (455,528,697), (464,777,905), (468,595,757), (473,864,985), (481,600,769), (504,703,865), (533,756,925), (540,629,829), (555,572,797), (580,741,941), (615,728,953), (616,663,905), (696,697,985).
Click here for the list of all Pythagorean triples containing no members greater than 10,000.
[15-May-2003]
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