Let $a$ and $b$ be positive integers such that $ab + 1$ divides $a^{2} + b^{2}$. Show that $$ \frac {a^{2} + b^{2}}{ab + 1} $$ is the square of an integer.
It's Olympiad question, any help?
Let $a$ and $b$ be positive integers such that $ab + 1$ divides $a^{2} + b^{2}$. Show that $$ \frac {a^{2} + b^{2}}{ab + 1} $$ is the square of an integer.
It's Olympiad question, any help?