Question 66
Let $N$ be the set of positive integers. Determine all functions $f : N \to N$ such that, for all positive integers $m$ and $n$,
$$
f^{f(n)}(m) + mn = f(m)f(n).
$$
Note that $f^k(n) = \underbrace{f(f(\cdots f(n)\cdots))}_{k \text{ times}}$.
$$
f^{f(n)}(m) + mn = f(m)f(n).
$$
Note that $f^k(n) = \underbrace{f(f(\cdots f(n)\cdots))}_{k \text{ times}}$.