ILL 1992 Problem 2

Let $m$ be a positive integer and $x_0, y_0$ integers such that $x_0, y_0$ are relatively prime, $y_0$ divides $x_0^2+m$ , and $x_0$ divides $y_0^2+m$ . Prove that there exist positive integers $x$ and $y$ such that $x$ and $y$ are relatively prime, $y$ divides $x^2 + m$ , $x$ divides $y^2 + m$ , and $x + y \leq m+ 1.$