Question 168
Find all functions $f: \mathbb{Z}_{\gt 0} \to \mathbb{Z}_{\gt 0}$ such that for all positive integers $m$ and $n$ it holds that
$$
(f(m))^2 + 2mf(n) + f(n^2)
$$
is the square of an integer.
$$
(f(m))^2 + 2mf(n) + f(n^2)
$$
is the square of an integer.