MathNet 2025 — 50 problems — Part 01 Question 13

Find all functions $f: \mathbb{Z}^+ \to \mathbb{Z}^+$, where $\mathbb{Z}^+$ is the set of all positive integers, such that for any positive integers $m, n$, $f^{f(m)}(n) + n = f^m(n) + f(n)$. Here powers of the function denote iteration.