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.

Let Y=(X+1), then:

(X^2 + 1) ((X+1)^2 + 1) -1 = (X^2+X+1)^2

More interestingly, let Y= 2X^2, then

(X^2+1)((2X^2)^2+1)-1 = (2X^3+X)^2

Posted by broll on 2016-06-10 08:02:21