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