Question 128
Let $\mathbb{N}_0$ be the set of nonnegative integers. Find all functions $f : \mathbb{N}_0 \to \mathbb{N}_0$ satisfying the equation
$$
f^{f(m)}(n) = n + 2f(m)
$$
for all $m, n \in \mathbb{N}_0$ such that $m \le n$.
$$
f^{f(m)}(n) = n + 2f(m)
$$
for all $m, n \in \mathbb{N}_0$ such that $m \le n$.