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