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.

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
(7^2+1)(98^2+1)=693^2+1
Edited on June 11, 2016, 12:52 pm

Posted by armando on 2016-06-11 11:04:10