Question 126
Let $\mathbb{N}$ be the set of positive integers. Find all functions $g: \mathbb{N} \to \mathbb{N}$ such that for all $m, n \in \mathbb{N}$ the number
$$
(g(m) + n)(m + g(n))
$$
is a perfect square.
$$
(g(m) + n)(m + g(n))
$$
is a perfect square.