List of Pythagorean Triples
Below is a list of Pythagorean Triples. The triples in this list are by no means exhaustive in nature because there are infinite numbers of Pythagorean Triples.
The Pythagorean Triples here are also called Primitive Pythagorean Triples because the Greatest Common Divisor (GCD) or the Greatest Common Factor (GCF) of the three positive integers is equal to 1.
Suppose we have a set of three (3) positive integers,
[latex]\left( {a,b,c} \right)[/latex]
they are Pythagorean Triples if it satisfies the equation,
[latex]{a^2} + {b^2} = {c^2}[/latex]
where the GCD of [latex]a,b,c[/latex] equals [latex]1[/latex].
It also implies that [latex]a,b[/latex] and [latex]c[/latex] are relatively prime numbers which simply means that their Greatest Common Factor is [latex]1[/latex].
List of Primitive Pythagorean Triples
(3, 4, 5)
[latex]{3^2} + {4^2} = {5^2}[/latex]
[latex]9 + 16 = 25[/latex]
[latex]25 = 25[/latex]
(5, 12, 13)
[latex]{5^2} + {12^2} = {13^2}[/latex]
[latex]25 + 144 = 169[/latex]
[latex]169 = 169[/latex]
(7, 24, 25)
[latex]{7^2} + {24^2} = {25^2}[/latex]
[latex]49 + 576 = 625[/latex]
[latex]625 = 625[/latex]
(8, 15, 17)
[latex]{8^2} + {15^2} = {17^2}[/latex]
[latex]64+225=289[/latex]
[latex]289=289[/latex]
(9, 40, 41)
[latex]{9^2} + {40^2} = {41^2}[/latex]
[latex]81 + 1,600 = 1,681[/latex]
[latex]1,681 = 1,681[/latex]
(11, 60, 61)
[latex]{11^2} + {60^2} = {61^2}[/latex]
[latex]121 + 3,600 = 3,721[/latex]
[latex]3,721 = 3,721[/latex]
(12, 35, 37)
[latex]{12^2} + {35^2} = {37^2}[/latex]
[latex]144 + 1,225 = 1,369[/latex]
[latex]1,369 = 1,369[/latex]
(13, 84, 85)
[latex]{13^2} + {84^2} = {85^2}[/latex]
[latex]169 + 7,056 = 7,225[/latex]
[latex]7,225 = 7,225[/latex]
(15, 112, 113)
[latex]{15^2} + {112^2} = {113^2}[/latex]
[latex]225 + 12,544 = 12,769[/latex]
[latex]12,769 = 12,769[/latex]
(16, 63, 65)
[latex]{16^2} + {63^2} = {65^2}[/latex]
[latex]256 + 3,969 = 4,225[/latex]
[latex]4,225 = 4,225[/latex]
(17, 144, 145)
[latex]{17^2} + {144^2} = {145^2}[/latex]
[latex]289 + 20,736 = 21,025[/latex]
[latex]21,025 = 21,025[/latex]
(19, 180, 181)
[latex]{19^2} + {180^2} = {181^2}[/latex]
[latex]361 + 32,400 = 32,761[/latex]
[latex]32,761 = 32,761[/latex]
(20, 21, 29)
[latex]{20^2} + {21^2} = {29^2}[/latex]
[latex]400 + 441 = 841[/latex]
[latex]841 = 841[/latex]
(20, 99, 101)
[latex]{20^2} + {99^2} = {101^2}[/latex]
[latex]400 + 9,801 = 10,201[/latex]
[latex]10,201 = 10,201[/latex]
(21, 220, 221)
[latex]{21^2} + {220^2} = {221^2}[/latex]
[latex]441 + 48,400 = 48,841[/latex]
[latex]48,841 = 48,841[/latex]
(23, 264, 265)
[latex]{23^2} + {264^2} = {265^2}[/latex]
[latex]529 + 69,696 = 70,225[/latex]
[latex]70,225 = 70,225[/latex]
(24, 143, 145)
[latex]{24^2} + {143^2} = {145^2}[/latex]
[latex]576 + 20,449 = 21,025[/latex]
[latex]21,025 = 21,025[/latex]
(25, 312, 313)
[latex]{25^2} + {312^2} = {313^2}[/latex]
[latex]625 + 97,344 = 97,969[/latex]
[latex]97,969 = 97,969[/latex]
(27, 364, 365)
[latex]{27^2} + {364^2} = {365^2}[/latex]
[latex]729 + 132,496 = 133,225[/latex]
[latex]133,225 = 133,225[/latex]
(28, 45, 53)
[latex]{28^2} + {45^2} = {53^2}[/latex]
[latex]784 + 2,025 = 2,890[/latex]
[latex]2,890 = 2,890[/latex]
(28, 195, 197)
[latex]{28^2} + {195^2} = {197^2}[/latex]
[latex]784 + 38,025 = 38,809[/latex]
[latex]38,809 = 38,809[/latex]
(29, 420, 421)
[latex]{29^2} + {420^2} = {421^2}[/latex]
[latex]841 + 176,400 = 177,241[/latex]
[latex]177,241 = 177,241[/latex]
(31, 480, 481)
[latex]{31^2} + {480^2} = {481^2}[/latex]
[latex]961 + 230,400 = 231,361[/latex]
[latex]231,361 = 231,361[/latex]
(32, 255, 257)
[latex]{32^2} + {255^2} = {257^2}[/latex]
[latex]1,024 + 65,025 = 66,049[/latex]
[latex]66,049 = 66,049[/latex]
(33, 56, 65)
[latex]{33^2} + {56^2} = {65^2}[/latex]
[latex]1,089 + 3,136 = 4,225[/latex]
[latex]4,225 = 4,225[/latex]
(33, 544, 545)
[latex]{33^2} + {544^2} = {545^2}[/latex]
[latex]1,089 + 295,936 = 297,025[/latex]
[latex]297,025 = 297,025[/latex]
(35, 612, 613)
[latex]{35^2} + {612^2} = {613^2}[/latex]
[latex]1,225 + 374,544 = 375,769[/latex]
[latex]375,769 = 375,769[/latex]
(36, 77, 85)
[latex]{36^2} + {77^2} = {85^2}[/latex]
[latex]1,296 + 5,929 = 7,225[/latex]
[latex]7,225 = 7,225[/latex]
(36, 323, 325)
[latex]{36^2} + {323^2} = {325^2}[/latex]
[latex]1,296 + 104,439 = 105,625[/latex]
[latex]105,625 = 105,625[/latex]
(37, 684, 685)
[latex]{37^2} + {684^2} = {685^2}[/latex]
[latex]1,369 + 467,856 = 469,225[/latex]
[latex]469,225 = 469,225[/latex]
(39, 80, 89)
[latex]{39^2} + {80^2} = {89^2}[/latex]
[latex]1,521 + 6,400 = 7,921[/latex]
[latex]7,921 = 7,921[/latex]
(39, 760, 761)
[latex]{39^2} + {760^2} = {761^2}[/latex]
[latex]1,521 + 577,600 = 579,121[/latex]
[latex]579,121 = 579,121[/latex]
(41, 840, 841)
[latex]{41^2} + {840^2} = {841^2}[/latex]
[latex]1,681 + 705,600 = 707,281[/latex]
[latex]707,281 = 707,281[/latex]
(43, 924, 925)
[latex]{43^2} + {924^2} = {925^2}[/latex]
[latex]1,849 + 853,776 = 855,625[/latex]
[latex]855,625 = 855,625[/latex]
(44, 117, 125)
[latex]{44^2} + {117^2} = {125^2}[/latex]
[latex]1,936 + 13,689 = 15,625[/latex]
[latex]15,625 = 15,625[/latex]
(45, 1012, 1013)
[latex]{45^2} + {1,012^2} = {1,013^2}[/latex]
[latex]2,025 + 1,024,144 = 1,026,169[/latex]
[latex]1,026,169 = 1,026,169[/latex]
(47, 1104, 1105)
[latex]{47^2} + {1,104^2} = {1,105^2}[/latex]
[latex]2,209 + 1,218,816 = 1,221,025[/latex]
[latex]1,221,025 = 1,221,025[/latex]
(48, 55, 73)
[latex]{48^2} + {55^2} = {73^2}[/latex]
[latex]2,304 + 3,025 = 5,329[/latex]
[latex]5,329 = 5,329[/latex]
(49, 1200, 1201)
[latex]{49^2} + {1,200^2} = {1,201^2}[/latex]
[latex]2,401 + 1,440,000 = 1,442,401[/latex]
[latex]1,442,401 = 1,442,401[/latex]
(51, 140, 149)
[latex]{51^2} + {140^2} = {149^2}[/latex]
[latex]2,601 + 19,600 = 22,201[/latex]
[latex]22,201 = 22,201[/latex]
(52, 165, 173)
[latex]{52^2} + {165^2} = {173^2}[/latex]
[latex]2,704 + 27,225 = 29,929[/latex]
[latex]29,929 = 29,929[/latex]
(57, 176, 185)
[latex]{57^2} + {176^2} = {185^2}[/latex]
[latex]3,249 + 30,976 = 34,225[/latex]
[latex]34,225 = 34,225[/latex]
(60, 91, 109)
[latex]{60^2} + {91^2} = {109^2}[/latex]
[latex]3,600 + 8,281 = 11,881[/latex]
[latex]11,881 = 11,881[/latex]
(60, 221, 229)
[latex]{60^2} + {221^2} = {229^2}[/latex]
[latex]3,600 + 48,841 = 52,441[/latex]
[latex]52,441 = 52,441[/latex]
(65, 72, 97)
[latex]{65^2} + {72^2} = {97^2}[/latex]
[latex]4,225 + 5,184 = 9,409[/latex]
[latex]9,409 = 9,409[/latex]
(68, 285, 293)
[latex]{68^2} + {285^2} = {293^2}[/latex]
[latex]4,624 + 81,225 = 85,849[/latex]
[latex]85,849 = 85,849[/latex]
(69, 260, 269)
[latex]{69^2} + {260^2} = {269^2}[/latex]
[latex]4,761 + 67,600 = 72,361[/latex]
[latex]72,361 = 72,361[/latex]
(84, 187, 205)
[latex]{84^2} + {187^2} = {205^2}[/latex]
[latex]7,056 + 34,969 = 42,025[/latex]
[latex]42,025 = 42,025[/latex]
(85, 132, 157)
[latex]{85^2} + {132^2} = {157^2}[/latex]
[latex]7,225 + 174,424 = 24,649[/latex]
[latex]24,649 = 24,649[/latex]
(88, 105, 137)
[latex]{88^2} + {105^2} = {137^2}[/latex]
[latex]7,744 + 11,025 = 18,769[/latex]
[latex]18,769 = 18,769[/latex]
(95, 168, 193)
[latex]{95^2} + {168^2} = {193^2}[/latex]
[latex]9,025 + 28,224 = 37,249[/latex]
[latex]37,249 = 37,249[/latex]
(96, 247, 265)
[latex]{96^2} + {247^2} = {265^2}[/latex]
[latex]9,216 + 61,009 = 70,225[/latex]
[latex]70,225 = 70,225[/latex]
(104, 153, 185)
[latex]{104^2} + {153^2} = {185^2}[/latex]
[latex]10,816 + 23,409 = 34,225[/latex]
[latex]34,225 = 34,225[/latex]
(105, 208, 233)
[latex]{105^2} + {208^2} = {233^2}[/latex]
[latex]11,025 + 43,264 = 54,289[/latex]
[latex]54,289 = 54,289[/latex]
(115, 252, 277)
[latex]{115^2} + {252^2} = {277^2}[/latex]
[latex]13,225 + 63,504 = 76,729[/latex]
[latex]76,729 = 76,729[/latex]
(119, 120, 169)
[latex]{119^2} + {120^2} = {169^2}[/latex]
[latex]14,161 + 14,400 = 28,561[/latex]
[latex]28,561 = 28,561[/latex]
(120, 209, 241)
[latex]{120^2} + {209^2} = {241^2}[/latex]
[latex]14,400 + 43,681 = 58,081[/latex]
[latex]58,081 = 58,081[/latex]
(133, 156, 205)
[latex]{133^2} + {156^2} = {205^2}[/latex]
[latex]17,689 + 24,336 = 42,025[/latex]
[latex]42,025 = 42,025[/latex]
(136, 273, 305)
[latex]{136^2} + {273^2} = {305^2}[/latex]
[latex]18,496 + 74,529 = 93,025[/latex]
[latex]93,025 = 93,025[/latex]
(140, 171, 221)
[latex]{140^2} + {171^2} = {221^2}[/latex]
[latex]19,600 + 29,241 = 48,841[/latex]
[latex]48,841 = 48,841[/latex]
(160, 231, 281)
[latex]{160^2} + {231^2} = {281^2}[/latex]
[latex]25,600 + 53,361 = 78,961[/latex]
[latex]78,961 = 78,961[/latex]
(161, 240, 289)
[latex]{161^2} + {240^2} = {289^2}[/latex]
[latex]25,921 + 57,600 = 83,521[/latex]
[latex]83,521 = 83,521[/latex]
(175, 288, 337)
[latex]{175^2} + {288^2} = {337^2}[/latex]
[latex]30,625 + 82,944 = 113,569[/latex]
[latex]113,569 = 113,569[/latex]
(180, 299, 349)
[latex]{180^2} + {299^2} = {349^2}[/latex]
[latex]32,400 + 89,401 = 121,801[/latex]
[latex]121,801 = 121,801[/latex]
(204, 253, 325)
[latex]{204^2} + {253^2} = {325^2}[/latex]
[latex]41,616 + 64,009 = 105,625[/latex]
[latex]105,625 = 105,625[/latex]
(207, 224, 305)
[latex]{207^2} + {224^2} = {305^2}[/latex]
[latex]42,849 + 50,176 = 93,025[/latex]
[latex]93,025 = 93,025[/latex]
(225, 272, 353)
[latex]{225^2} + {272^2} = {353^2}[/latex]
[latex]50,625 + 73,984 = 124,609[/latex]
[latex]124,609 = 124,609[/latex]
(252, 275, 373)
[latex]{252^2} + {275^2} = {373^2}[/latex]
[latex]63,504 + 75,625 = 139,129[/latex]
[latex]139,129 = 139,129[/latex]
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