x^2 + y^2 = z^3, with z < 100

 
 
x^2 + y^2 = z^3

x, y, z   are distinct positive integers and   z < 100
 

   2^3 = 2^2 + 2^2
   5^3 = 5^2 + 10^2 = 2^2 + 11^2
   8^3 = 16^2 + 16^2

  10^3 = 10^2 + 30^2 = 18^2 + 26^2
  13^3 = 9^2 + 46^2 = 26^2 + 39^2
  17^3 = 17^2 + 68^2 = 47^2 + 52^2
  18^3 = 54^2 + 54^2

  20^3 = 40^2 + 80^2 = 16^2 + 88^2
  25^3 = 75^2 + 100^2 = 44^2 + 117^2 = 35^2 + 120^2
  26^3 = 26^2 + 130^2 = 74^2 + 110^2
  29^3 = 65^2 + 142^2 = 58^2 + 145^2

  32^3 = 128^2 + 128^2
  34^3 = 10^2 + 198^2 = 102^2 + 170^2
  37^3 = 37^2 + 222^2 = 107^2 + 198^2

  40^3 = 80^2 + 240^2 = 144^2 + 208^2
  41^3 = 115^2 + 236^2 = 164^2 + 205^2
  45^3 = 54^2 + 297^2 = 135^2 + 270^2

  50^3 = 50^2 + 350^2 = 146^2 + 322^2 = 170^2 + 310^2 = 250^2 + 250^2
  52^3 = 72^2 + 368^2 = 208^2 + 312^2
  53^3 = 106^2 + 371^2 = 259^2 + 286^2
  58^3 = 154^2 + 414^2 = 174^2 + 406^2

  61^3 = 234^2 + 415^2 = 305^2 + 366^2
  65^3 = 7^2 + 524^2
  65^3 = 65^2 + 520^2
  65^3 = 140^2 + 505^2
  65^3 = 191^2 + 488^2
  65^3 = 208^2 + 481^2
  65^3 = 260^2 + 455^2
  65^3 = 320^2 + 415^2
  65^3 = 364^2 + 377^2
  68^3 = 136^2 + 544^2 = 376^2 + 416^2

  72^3 = 432^2 + 432^2
  73^3 = 219^2 + 584^2 = 296^2 + 549^2
  74^3 = 182^2 + 610^2 = 370^2 + 518^2

  80^3 = 320^2 + 640^2
  82^3 = 82^2 + 738^2 = 242^2 + 702^2
  85^3 = 51^2 + 782^2
  85^3 = 170^2 + 765^2
  85^3 = 210^2 + 755^2
  85^3 = 285^2 + 730^2
  85^3 = 323^2 + 714^2
  85^3 = 413^2 + 666^2
  85^3 = 478^2 + 621^2
  85^3 = 510^2 + 595^2
  89^3 = 88^2 + 835^2 = 445^2 + 712^2

  90^3 = 270^2 + 810^2
  97^3 = 388^2 + 873^2 = 297^2 + 908^2
  98^3 = 686^2 + 686^2

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged , . Bookmark the permalink.

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