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[parent] first primitive Pythagorean triplets (Example)

$ ($odd cathetus$ )^2+($even cathetus$ )^2 = ($hypotenuse$ )^2$

$ 3^2+4^2 = 5^2 $    ( $ \leftarrow$ here the so-called Egyptian numbers, known by the pyramid builders)
$ 5^2+12^2 = 13^2 $
$ 15^2+8^2 = 17^2 $
$ 7^2+24^2 = 25^2 $
$ 21^2+20^2 = 29^2 $
$ 9^2+40^2 = 41^2 $
$ 35^2+12^2 = 37^2 $
$ 11^2+60^2 = 61^2 $
$ 45^2+28^2 = 53^2 $
$ 33^2+56^2 = 65^2 $
$ 13^2+84^2 = 85^2 $
$ 63^2+16^2 = 65^2 $
$ 55^2+48^2 = 73^2 $
$ 39^2+80^2 = 89^2 $
$ 15^2+112^2 = 113^2 $
$ 77^2+36^2 = 85^2 $
$ 65^2+72^2 = 97^2 $
$ 17^2+144^2 = 145^2 $
$ 99^2+20^2 = 101^2 $
$ 91^2+60^2 = 109^2 $
$ 51^2+140^2 = 149^2 $
$ 19^2+180^2 = 181^2 $
$ 117^2+44^2 = 125^2 $
$ 105^2+88^2 = 137^2 $
$ 85^2+132^2 = 157^2 $
$ 57^2+176^2 = 185^2 $
$ 21^2+220^2 = 221^2 $
$ 143^2+24^2 = 145^2 $
$ 119^2+120^2 = 169^2 $
$ 95^2+168^2 = 193^2 $
$ 23^2+264^2 = 265^2 $
$ 165^2+52^2 = 173^2 $
$ 153^2+104^2 = 185^2 $
$ 133^2+156^2 = 205^2 $
$ 105^2+208^2 = 233^2 $
$ 69^2+260^2 = 269^2 $
$ 25^2+312^2 = 313^2 $
$ 195^2+28^2 = 197^2 $
$ 187^2+84^2 = 205^2 $
$ 171^2+140^2 = 221^2 $
$ 115^2+252^2 = 277^2 $
$ 75^2+308^2 = 317^2 $
$ 27^2+364^2 = 365^2 $
$ 221^2+60^2 = 229^2 $
$ 209^2+120^2 = 241^2 $
$ 161^2+240^2 = 289^2 $
$ 29^2+420^2 = 421^2 $
$ 255^2+32^2 = 257^2 $
$ 247^2+96^2 = 265^2 $
$ 231^2+160^2 = 281^2 $
$ 207^2+224^2 = 305^2 $
$ 175^2+288^2 = 337^2 $
$ 135^2+352^2 = 377^2 $
$ 87^2+416^2 = 425^2 $
$ 31^2+480^2 = 481^2 $
$ 285^2+68^2 = 293^2 $
$ 273^2+136^2 = 305^2 $
$ 253^2+204^2 = 325^2 $
$ 225^2+272^2 = 353^2 $
$ 189^2+340^2 = 389^2 $
$ 145^2+408^2 = 433^2 $
$ 93^2+476^2 = 485^2 $
$ 33^2+544^2 = 545^2 $
$ 323^2+36^2 = 325^2 $
$ 299^2+180^2 = 349^2 $
$ 275^2+252^2 = 373^2 $
$ 203^2+396^2 = 445^2 $
$ 155^2+468^2 = 493^2 $
$ 35^2+612^2 = 613^2 $
$ 357^2+76^2 = 365^2 $
$ 345^2+152^2 = 377^2 $
$ 325^2+228^2 = 397^2 $
$ 297^2+304^2 = 425^2 $
$ 261^2+380^2 = 461^2 $
$ 217^2+456^2 = 505^2 $
$ 165^2+532^2 = 557^2 $
$ 105^2+608^2 = 617^2 $
$ 37^2+684^2 = 685^2 $
$ 399^2+40^2 = 401^2 $
$ 391^2+120^2 = 409^2 $
$ 351^2+280^2 = 449^2 $
$ 319^2+360^2 = 481^2 $
$ 279^2+440^2 = 521^2 $
$ 231^2+520^2 = 569^2 $
$ 111^2+680^2 = 689^2 $
$ 39^2+760^2 = 761^2 $
$ 437^2+84^2 = 445^2 $
$ 425^2+168^2 = 457^2 $
$ 377^2+336^2 = 505^2 $
$ 341^2+420^2 = 541^2 $
$ 185^2+672^2 = 697^2 $
$ 41^2+840^2 = 841^2 $
$ 483^2+44^2 = 485^2 $
$ 475^2+132^2 = 493^2 $
$ 459^2+220^2 = 509^2 $
$ 435^2+308^2 = 533^2 $
$ 403^2+396^2 = 565^2 $
$ 315^2+572^2 = 653^2 $
$ 259^2+660^2 = 709^2 $
$ 195^2+748^2 = 773^2 $
$ 123^2+836^2 = 845^2 $
$ 43^2+924^2 = 925^2 $
$ 525^2+92^2 = 533^2 $
$ 513^2+184^2 = 545^2 $
$ 493^2+276^2 = 565^2 $
$ 465^2+368^2 = 593^2 $
$ 429^2+460^2 = 629^2 $
$ 385^2+552^2 = 673^2 $
$ 333^2+644^2 = 725^2 $
$ 273^2+736^2 = 785^2 $
$ 205^2+828^2 = 853^2 $
$ 129^2+920^2 = 929^2 $
$ 45^2+1012^2 = 1013^2 $
$ 575^2+48^2 = 577^2 $
$ 551^2+240^2 = 601^2 $
$ 527^2+336^2 = 625^2 $
$ 455^2+528^2 = 697^2 $
$ 407^2+624^2 = 745^2 $
$ 287^2+816^2 = 865^2 $
$ 215^2+912^2 = 937^2 $
$ 47^2+1104^2 = 1105^2 $
$ 621^2+100^2 = 629^2 $
$ 609^2+200^2 = 641^2 $
$ 589^2+300^2 = 661^2 $
$ 561^2+400^2 = 689^2 $
$ 481^2+600^2 = 769^2 $
$ 429^2+700^2 = 821^2 $
$ 369^2+800^2 = 881^2 $
$ 301^2+900^2 = 949^2 $
$ 141^2+1100^2 = 1109^2 $
$ 49^2+1200^2 = 1201^2 $
$ 675^2+52^2 = 677^2 $
$ 667^2+156^2 = 685^2 $
$ 651^2+260^2 = 701^2 $
$ 627^2+364^2 = 725^2 $
$ 595^2+468^2 = 757^2 $
$ 555^2+572^2 = 797^2 $
$ 451^2+780^2 = 901^2 $
$ 387^2+884^2 = 965^2 $
$ 315^2+988^2 = 1037^2 $
$ 235^2+1092^2 = 1117^2 $
$ 147^2+1196^2 = 1205^2 $
$ 51^2+1300^2 = 1301^2 $
$ 725^2+108^2 = 733^2 $
$ 713^2+216^2 = 745^2 $
$ 665^2+432^2 = 793^2 $
$ 629^2+540^2 = 829^2 $
$ 533^2+756^2 = 925^2 $
$ 473^2+864^2 = 985^2 $
$ 329^2+1080^2 = 1129^2 $
$ 245^2+1188^2 = 1213^2 $
$ 53^2+1404^2 = 1405^2 $

N.B. that the lengths of the even cathetus and the hypotenuse are consecutive integers (as 1404 and 1405) always when the corresponding seed numbers $ m$ and $ n$ (see the parent entry) are successive integers.



"first primitive Pythagorean triplets" is owned by pahio.
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See Also: Pythagorean theorem, incircle radius determined by Pythagorean triple

Other names:  least coprime Pythagorean triplets
Also defines:  Egyptian numbers
Keywords:  right triangle, integers

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Cross-references: integers, pyramid
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This is version 7 of first primitive Pythagorean triplets, born on 2005-08-03, modified 2006-12-27.
Object id is 7289, canonical name is FirstPrimitivePythagoreanTriplets.
Accessed 1987 times total.

Classification:
AMS MSC: 11-00 (Number theory :: General reference works )
 01A16 (History and biography :: History of mathematics and mathematicians :: Egyptian)
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