# Thread: A divisibility problem 3

1. ## A divisibility problem 3

Let $a$ and $b$ be positive integers such that $(1+ab)|(a^2+b^2)$. Show that the integer $(a^2+b^2)/(1+ab)$ must be a perfect square.

2. Originally Posted by eyke
Let $a$ and $b$ be positive integers such that $(1+ab)|(a^2+b^2)$. Show that the integer $(a^2+b^2)/(1+ab)$ must be a perfect square.
see question #6 in IMO 1988.