Question 3
Find all functions $g \colon \mathbb{Z}_{\gt 0} \to \mathbb{Z}_{\gt 0}$ such that $$
\left( g(m)+n \right)\left( g(n)+m \right)
$$ is a perfect square for every pair of positive integers $m,n$.
\left( g(m)+n \right)\left( g(n)+m \right)
$$ is a perfect square for every pair of positive integers $m,n$.