Lista de triples pitagóricos

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Pau Monfort
@paumonfort
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Lista de triples pitagóricos

A continuación hay una lista de Triples pitagóricos. Los triples en esta lista no son de ninguna manera exhaustivos por naturaleza porque hay un número infinito de Triples pitagóricos.



Los Triples pitagóricos aquí también se llaman Triples pitagóricos primitivos porque el Divisor Común Máximo (GCD) o el máximo común divisor (GCF) de los tres enteros positivos es igual a 1.

Supongamos que tenemos un conjunto de tres (3) enteros positivos,


izquierda ({a, b, c} derecha)

son Triples pitagóricos si satisface la ecuación,

{a ^ 2} + {b ^ 2} = {c ^ 2}

donde el GCD de a, b, c es igual a 1.

También implica que a, byc son números primos relativos, lo que simplemente significa que su Máximo Común Factor es 1.

Lista de triples pitagóricas primitivos

(3, 4, 5)

{3 ^ 2} + {4 ^ 2} = {5 ^ 2} 9 + 16 = 25 25 = 25

(5, 12, 13)

{5 ^ 2} + {12 ^ 2} = {13 ^ 2} 25 + 144 = 169 169 = 169

(7, 24, 25)

{7 ^ 2} + {24 ^ 2} = {25 ^ 2} 49 + 576 = 625 625 = 625

(8, 15, 17)


{8^2} + {15^2} = {17^2} 64+225=289 289=289

(9, 40, 41)

{9 ^ 2} + {40 ^ 2} = {41 ^ 2} 81 + 1,600 = 1,681 1,681 = 1,681

(11, 60, 61)

{11 ^ 2} + {60 ^ 2} = {61 ^ 2} 121 + 3,600 = 3,721 3,721 = 3,721

(12, 35, 37)

{12 ^ 2} + {35 ^ 2} = {37 ^ 2} 144 + 1,225 = 1,369 1,369 = 1,369

(13, 84, 85)

{13 ^ 2} + {84 ^ 2} = {85 ^ 2} 169 + 7,056 = 7,225 7,225 = 7,225

(15, 112, 113)

{15 ^ 2} + {112 ^ 2} = {113 ^ 2} 225 + 12,544 = 12,769 12,769 = 12,769

(16, 63, 65)

{16 ^ 2} + {63 ^ 2} = {65 ^ 2} 256 + 3,969 = 4,225 4,225 = 4,225

(17, 144, 145)

{17 ^ 2} + {144 ^ 2} = {145 ^ 2} 289 + 20,736 = 21,025 21,025 = 21,025

(19, 180, 181)

{19 ^ 2} + {180 ^ 2} = {181 ^ 2} 361 + 32,400 = 32,761 32,761 = 32,761

(20, 21, 29)


{20 ^ 2} + {21 ^ 2} = {29 ^ 2} 400 + 441 = 841 841 = 841

(20, 99, 101)

{20 ^ 2} + {99 ^ 2} = {101 ^ 2} 400 + 9,801 = 10,201 10,201 = 10,201

(21, 220, 221)


{21 ^ 2} + {220 ^ 2} = {221 ^ 2} 441 + 48,400 = 48,841 48,841 = 48,841

(23, 264, 265)

{23 ^ 2} + {264 ^ 2} = {265 ^ 2} 529 + 69,696 = 70,225 70,225 = 70,225

(24, 143, 145)

{24 ^ 2} + {143 ^ 2} = {145 ^ 2} 576 + 20,449 = 21,025 21,025 = 21,025

(25, 312, 313)

{25 ^ 2} + {312 ^ 2} = {313 ^ 2} 625 + 97,344 = 97,969 97,969 = 97,969

(27, 364, 365)

{27 ^ 2} + {364 ^ 2} = {365 ^ 2} 729 + 132,496 = 133,225 133,225 = 133,225

(28, 45, 53)

{28 ^ 2} + {45 ^ 2} = {53 ^ 2} 784 + 2,025 = 2,890 2,890 = 2,890

(28, 195, 197)

{28 ^ 2} + {195 ^ 2} = {197 ^ 2} 784 + 38,025 = 38,809 38,809 = 38,809

(29, 420, 421)

{29 ^ 2} + {420 ^ 2} = {421 ^ 2} 841 + 176,400 = 177,241 177,241 = 177,241

(31, 480, 481)

{31 ^ 2} + {480 ^ 2} = {481 ^ 2} 961 + 230,400 = 231,361 231,361 = 231,361

(32, 255, 257)

{32 ^ 2} + {255 ^ 2} = {257 ^ 2} 1,024 + 65,025 = 66,049 66,049 = 66,049

(33, 56, 65)

{33 ^ 2} + {56 ^ 2} = {65 ^ 2} 1,089 + 3,136 = 4,225 4,225 = 4,225

(33, 544, 545)


{33 ^ 2} + {544 ^ 2} = {545 ^ 2} 1,089 + 295,936 = 297,025 297,025 = 297,025

(35, 612, 613)

{35 ^ 2} + {612 ^ 2} = {613 ^ 2} 1,225 + 374,544 = 375,769 375,769 = 375,769

(36, 77, 85)

{36 ^ 2} + {77 ^ 2} = {85 ^ 2} 1,296 + 5,929 = 7,225 7,225 = 7,225

(36, 323, 325)


{36 ^ 2} + {323 ^ 2} = {325 ^ 2} 1,296 + 104,439 = 105,625 105,625 = 105,625

(37, 684, 685)

{37 ^ 2} + {684 ^ 2} = {685 ^ 2} 1,369 + 467,856 = 469,225 469,225 = 469,225

(39, 80, 89)

{39 ^ 2} + {80 ^ 2} = {89 ^ 2} 1,521 + 6,400 = 7,921 7,921 = 7,921

(39, 760, 761)

{39 ^ 2} + {760 ^ 2} = {761 ^ 2} 1,521 + 577,600 = 579,121 579,121 = 579,121

(41, 840, 841)

{41 ^ 2} + {840 ^ 2} = {841 ^ 2} 1,681 + 705,600 = 707,281 707,281 = 707,281

(43, 924, 925)

{43 ^ 2} + {924 ^ 2} = {925 ^ 2} 1,849 + 853,776 = 855,625 855,625 = 855,625

(44, 117, 125)

{44 ^ 2} + {117 ^ 2} = {125 ^ 2} 1,936 + 13,689 = 15,625 15,625 = 15,625

(45, 1012, 1013)

{45 ^ 2} + {1,012 ^ 2} = {1,013 ^ 2} 2,025 + 1,024,144 = 1,026,169 1,026,169 = 1,026,169

(47, 1104, 1105)

{47 ^ 2} + {1,104 ^ 2} = {1,105 ^ 2} 2,209 + 1,218,816 = 1,221,025 1,221,025 = 1,221,025

(48, 55, 73)

{48 ^ 2} + {55 ^ 2} = {73 ^ 2} 2,304 + 3,025 = 5,329 5,329 = 5,329

(49, 1200, 1201)

{49 ^ 2} + {1,200 ^ 2} = {1,201 ^ 2} 2,401 + 1,440,000 = 1,442,401 1,442,401 = 1,442,401

(51, 140, 149)

{51 ^ 2} + {140 ^ 2} = {149 ^ 2} 2,601 + 19,600 = 22,201 22,201 = 22,201

(52, 165, 173)

{52 ^ 2} + {165 ^ 2} = {173 ^ 2} 2,704 + 27,225 = 29,929 29,929 = 29,929

(57, 176, 185)

{57 ^ 2} + {176 ^ 2} = {185 ^ 2} 3,249 + 30,976 = 34,225 34,225 = 34,225

(60, 91, 109)

{60 ^ 2} + {91 ^ 2} = {109 ^ 2} 3,600 + 8,281 = 11,881 11,881 = 11,881

(60, 221, 229)

{60 ^ 2} + {221 ^ 2} = {229 ^ 2} 3,600 + 48,841 = 52,441 52,441 = 52,441

(65, 72, 97)

{65 ^ 2} + {72 ^ 2} = {97 ^ 2} 4,225 + 5,184 = 9,409 9,409 = 9,409

(68, 285, 293)

{68 ^ 2} + {285 ^ 2} = {293 ^ 2} 4,624 + 81,225 = 85,849 85,849 = 85,849

(69, 260, 269)

{69 ^ 2} + {260 ^ 2} = {269 ^ 2} 4,761 + 67,600 = 72,361 72,361 = 72,361

(84, 187, 205)

{84 ^ 2} + {187 ^ 2} = {205 ^ 2} 7,056 + 34,969 = 42,025 42,025 = 42,025

(85, 132, 157)

{85 ^ 2} + {132 ^ 2} = {157 ^ 2} 7,225 + 174,424 = 24,649 24,649 = 24,649

(88, 105, 137)

{88 ^ 2} + {105 ^ 2} = {137 ^ 2} 7,744 + 11,025 = 18,769 18,769 = 18,769

(95, 168, 193)

{95 ^ 2} + {168 ^ 2} = {193 ^ 2} 9,025 + 28,224 = 37,249 37,249 = 37,249

(96, 247, 265)

{96 ^ 2} + {247 ^ 2} = {265 ^ 2} 9,216 + 61,009 = 70,225 70,225 = 70,225

(104, 153, 185)

{104 ^ 2} + {153 ^ 2} = {185 ^ 2} 10,816 + 23,409 = 34,225 34,225 = 34,225

(105, 208, 233)

{105 ^ 2} + {208 ^ 2} = {233 ^ 2} 11,025 + 43,264 = 54,289 54,289 = 54,289

(115, 252, 277)

{115 ^ 2} + {252 ^ 2} = {277 ^ 2} 13,225 + 63,504 = 76,729 76,729 = 76,729

(119, 120, 169)

{119 ^ 2} + {120 ^ 2} = {169 ^ 2} 14,161 + 14,400 = 28,561 28,561 = 28,561

(120, 209, 241)

{120 ^ 2} + {209 ^ 2} = {241 ^ 2} 14,400 + 43,681 = 58,081 58,081 = 58,081

(133, 156, 205)

{133 ^ 2} + {156 ^ 2} = {205 ^ 2} 17,689 + 24,336 = 42,025 42,025 = 42,025

(136, 273, 305)

{136 ^ 2} + {273 ^ 2} = {305 ^ 2} 18,496 + 74,529 = 93,025 93,025 = 93,025

(140, 171, 221)

{140 ^ 2} + {171 ^ 2} = {221 ^ 2} 19,600 + 29,241 = 48,841 48,841 = 48,841

(160, 231, 281)

{160 ^ 2} + {231 ^ 2} = {281 ^ 2} 25,600 + 53,361 = 78,961 78,961 = 78,961

(161, 240, 289)

{161 ^ 2} + {240 ^ 2} = {289 ^ 2} 25,921 + 57,600 = 83,521 83,521 = 83,521

(175, 288, 337)

{175 ^ 2} + {288 ^ 2} = {337 ^ 2} 30,625 + 82,944 = 113,569 113,569 = 113,569

(180, 299, 349)

{180 ^ 2} + {299 ^ 2} = {349 ^ 2} 32,400 + 89,401 = 121,801 121,801 = 121,801

(204, 253, 325)

{204 ^ 2} + {253 ^ 2} = {325 ^ 2} 41,616 + 64,009 = 105,625 105,625 = 105,625

(207, 224, 305)

{207 ^ 2} + {224 ^ 2} = {305 ^ 2} 42,849 + 50,176 = 93,025 93,025 = 93,025

(225, 272, 353)

{225 ^ 2} + {272 ^ 2} = {353 ^ 2} 50,625 + 73,984 = 124,609 124,609 = 124,609

(252, 275, 373)

{252 ^ 2} + {275 ^ 2} = {373 ^ 2} 63,504 + 75,625 = 139,129 139,129 = 139,129

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