Problem

Source: IV International Festival of Young Mathematicians Sozopol 2013, Theme for 10-12 grade

Tags: number theory, Prime number, power of number, Divisibility



Let $a$ and $b$ be two distinct natural numbers. It is known that $a^2+b|b^2+a$ and that $b^2+a$ is a power of a prime number. Determine the possible values of $a$ and $b$.