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.
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.