Question 155
Let $p$ be an odd prime number, and $a$, $b$, $m$, $r$ be positive integers, such that $p \nmid ab$ and $ab \gt m^2$. Prove that there exists at most one pair of positive integers $(x, y)$ satisfying the following conditions: $x$ and $y$ are coprime, and $ax^2 + by^2 = mp^r$.