On a Quick Expansion Method for Pythagorus Triples

by Frank C. Fung ( 1st published in December, 2021. )

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Section XII - Results for the [ 8-15-17 / 12-35-37 ] Pair

Summary for the Section :

• In this Section , we shall present the results for the [ 8-15-17 / 12-35-37 ] pair ,
  • arising from the { Quick Expansion Procedure } as discussed in Part III of this paper .

Case 33 :

• For Case 33 , the values for { A, B, C } are :
  • A = +345 + 0i
  • B = -135 + 72i
  • C = -210 - 72i

  And the resultant Pythagorus Triple { X, Y, Z } is then :

  	Value of Number	Square of Number	Factors of Number
  X	262,689,851,756,304	69,005,958,215,748,971,713,403,740,416	16 x 729 x 7 x 23 x 1721 x 81281
  Y	409,215,574,627,200	167,457,386,517,469,492,418,979,840,000	16 x 729 x 8 x 9 x 25 x 11 x 43 x 89 x 463
  xxxxx	xxxxxxxxxxxxxxxxxxxxxxxxx	xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx	xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
  Z	486,274,968,236,304	236,463,344,733,218,464,132,383,580,416	16 x 729 x 13 x 29 x 101 x 409 x 2677

Case 34 :

• For Case 34, the values for { A, B, C } are :
  • A = +621 + 0i
  • B = -525 + 280i
  • C = -96 - 280i

  And the resultant Pythagorus Triple { X, Y, Z } is then :

  	Value of Number	Square of Number	Factors of Number
  X	201,099,491,885,321	40,441,005,636,534,286,727,015,273,041	23 x 97 x 199 x 599 x 756191
  Y	102,585,561,587,669,160	10,523,797,446,257,462,267,352,561,615,105,600	8 x 9 x 5 x 7 x 11 x 13 x 31 x 37 x 353 x 499 x 1409
  xxxxx	xxxxxxxxxxxxxxxxxxxxxxxxx	xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx	xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
  Z	102,585,758,696,142,121	10,523,837,887,263,098,801,639,288,630,378,641	17 x 73 x 401 x 347929 x 592489

Case 35 :

• For Case 35 , the values for the A, B and C are :
  • A = +92 + 0i
  • B = -56 + 105i
  • C = -36 - 105i

  And the resultant Pythagorus Triple { X, Y, Z } is then :

  	Value of Number	Square of Number	Factors of Number
  X	9,499,684,168,925	90,243,999,309,324,267,935,655,625	25 x 23 x 139 x 163 x 729187
  Y	3,251,962,583,100	10,575,260,641,882,424,405,610,000	25 x 4 x 9 x 7 x 11 x 4729 x 9923
  xxxxx	xxxxxxxxxxxxxxxxxxxxxxxxx	xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx	xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
  Z	10,040,879,441,125	100,819,259,951,206,692,341,265,625	25 x 5 x 13 x 17 x 89 x 149 x 27409

Case 36 :

• For Case 36, the values for the A, B and C are :
  • A = +207 + 0i
  • B = -32 + 60i
  • C = -175 - 60i

  And the resultant Pythagorus Triple { X, Y, Z } is then :

  	Value of Number	Square of Number	Factors of Number
  X	27,479,536,431,949	755,124,922,514,812,377,907,938,601	7 x 23 x 131 x 167 x 587 x 13291
  Y	74,174,057,125,740	5,501,790,750,492,540,870,170,547,600	4 x 9 x 5 x 11 x 13 x 19 x 71 x 719 x 2971
  xxxxx	xxxxxxxxxxxxxxxxxxxxxxxxx	xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx	xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
  Z	79,100,667,968,149	6,256,915,673,007,353,248,078,486,201	29 x 41 x 1289 x 1481 x 34849

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go to the next Section : Section XX - Results for the [ 20-21-29 / 12-35-37 ] Pythagorus-Triple Pair

go to the last Section : Section XVIII - Results for the [ 8-15-17 / 20-21-29 ] Pythagorus-Triple Pair

return to Pythagorus Triples Homepage

Original dated 2021-12-27