On a Quick Expansion Method for Pythagorus Triples

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

Top Of Page

Section XVII - Results for the [ 5-12-13 / 12-35-37 ] Pythagorus-Triple Pair

Summary for the Section :

• In this Section , we shall present the results for the [ 5-12-13 / 12-35-37 ] pair ,
  • arising from the { Quick Expansion Procedure } as discussed in Part III of this paper .

Case 25 :

• For Case 25 , the values for { A, B, C } are :
  • A = +40 + 0i
  • B = -5 + 12i
  • C = -35 - 12i

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

  	Value of Number	Square of Number	Factors of Number
  X	1,904,679,441	3,627,803,772,968,072,481	729 x 7 x 7 x 71 x 751
  Y	4,206,125,880	17,691,494,918,405,774,400	729 x 8 x 9 x 5 x 11 x 31 x 47
  xxxxx	xxxxxxxxxxxxxxxxxxxxxxxxx	xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx	xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
  Z	4,617,282,609	21,319,298,691,373,846,881	729 x 41 x 241 x 641

Case 26 :

• For Case 26, the values for { A, B, C } are :
  • A = +319 + 0i
  • B = -175 + 420i
  • C = -144 - 420i

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

  	Value of Number	Square of Number	Factors of Number
  X	28,744,798,163,945,219	826,263,421,485,948,433,319,558,832,957,961	509 x 1321 x 119759 x 356969
  Y	3,993,060,768,418,260	15,944,534,300,281,025,017,822,301,427,600	9 x 7 x 11 x 31 x 47 x 733 x 269761
  xxxxx	xxxxxxxxxxxxxxxxxxxxxxxxx	xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx	xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
  Z	29,020,819,350,704,581	842,207,955,786,229,458,337,381,134,385,561	53 x 73 x 89 x 101 x 1181 x 706561

Case 27 :

• For Case 27 , the values for the A, B and C are :
  • A = +96 + 0i
  • B = -84 + 35i
  • C = -12 - 35i

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

  	Value of Number	Square of Number	Factors of Number
  X	292,331,151,575	85,457,502,181,165,624,980,625	25 x 178 x 197 x 223 x 1487
  Y	1,052.748,635,400	1,108,279,689,336,562,133,160,000	25 x 4 x 27 x 7 x 11 x 23 x 31 x 53 x 67
  xxxxx	xxxxxxxxxxxxxxxxxxxxxxxxx	xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx	xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
  Z	1,092,582,807,625	1,193,737,191,517,727,758,140,625	25 x 5 x 269 x 2521 x 12889

Case 28 :

• For Case 28, the values for the A, B and C are :
  • A = +319 + 0i
  • B = -144 + 60i
  • C = -175 - 60i

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

  	Value of Number	Square of Number	Factors of Number
  X	179,718,400,106,819	32,298,703,336,954,679,550,610,298,761	7 x 2517583 x 10197899
  Y	103,287,919,959,180	10,668,394,409,493,974,212,866,272,400	4 x 9 x 5 x 11 x 23 x 31 x 41 x 127 x 14051
  xxxxx	xxxxxxxxxxxxxxxxxxxxxxxxx	xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx	xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
  Z	207,285,063,973,381	42,967,097,746,448,653,763,476,571,161	15361 x 61909 x 217969

go to Top Of Page

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

go to the last Section : Section XVI - Results for the [ 5-12-13 / 20-21-29 Pythagorus-Triple Pair

return to Pythagorus Triples Homepage

Original dated 2021-12-27