first primitive Pythagorean triplets
FirstPrimitivePythagoreanTriplets
2005-08-03 16:32:11
2006-12-27 08:57:27
Example
Pythagorean triplet
Egyptian numbers
right triangle
integers
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$(\mbox{odd cathetus})^2+(\mbox{even cathetus})^2 = (\mbox{hypotenuse})^2$\\
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$3^2+4^2 = 5^2 $\quad ($\leftarrow$ here the so-called {\em 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 \PMlinkname{parent}{PythagoreanTriple} entry) are successive integers.