ISL 1992 Problem 1

Prove that for any positive integer $m$ there exist an infinite number of pairs of integers $(x, y)$ such that

(i) $x$ and $y$ are relatively prime; (ii) $y$ divides $x^2 + m$ ; (iii) $x$ divides $y^2 + m.$ (iv) $x + y \leq m + 1-$ (optional condition)