Question:

Prove the following assertion: The system of simultaneous equations x^2+y^2=z^2-1 and x^2-y^2=w^2 has infinitely many solutions in positive integers x, y, z, w.

I was thinking I could consider that for any integer n>=1and then take x=2n^2 and y=2n, but I am not sure how that would work out.