I am preparing myself for my number theory midterm and I am stuck in this textbook question. I don't understand what question is asking. Any hint would be appreciated.
Prove that if $x$ is an integer then $x^3 + y^2 = z^2$ has a solution in integers $y$, $z$.
My attempt: $x^3 = z^2-y^2 = (z-y)(z+y)$, what is the next step?