Positive integers $a$ and $b$ are given such that each of the numbers $ab$ and $(a+1)(b+1)$ is a perfect square. Prove that there exists an integer $n>1$ such that the number $(a+n)(b+n)$ is a perfect square.
Source: 2017 Polish Junior Math Olympiad Finals
Tags: number theory
Positive integers $a$ and $b$ are given such that each of the numbers $ab$ and $(a+1)(b+1)$ is a perfect square. Prove that there exists an integer $n>1$ such that the number $(a+n)(b+n)$ is a perfect square.