Question:
Prove the following assertion: The system of simultaneous equations x^2+y^2=z^2-1 and X^2-y^2=w^2-1 has infinitely many solutions in positive integers x, y, z, w.
I was thinking I could consider that for any integer n>=1 and then take x=2n^2 and y=2n, but I am not sure.
Prove the following assertion: The system of simultaneous equations x^2+y^2=z^2-1 and X^2-y^2=w^2-1 has infinitely many solutions in positive integers x, y, z, w.
I was thinking I could consider that for any integer n>=1 and then take x=2n^2 and y=2n, but I am not sure.