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Infinitely Diophantine (Posted on 2016-06-10) Difficulty: 3 of 5
Each of X, Y and Z is a positive integer > 1 such that:

(X2 + 1) (Y2 + 1) = (Z2 + 1)

Does there exist an infinite number of solutions to the above equation?
Give reasons for your answer.

No Solution Yet Submitted by K Sengupta    
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No Subject Comment 2 of 2 |
From the equation comes
(xy)^2 + x^2 + y^2 = z^2

(xy)^2 + n^2 + 2nxy is a square for each value of n

Then when y=2x^2 or x=2y^2 z^2 will be square

For ex x=7 2x^2=98 Then if y=98, z will be square. For ex y=98
Edited on June 11, 2016, 12:52 pm
  Posted by armando on 2016-06-11 11:04:10
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