MathNet 2023-part-06 — 191 problems (EN–VI) Question 119

Denote the set of positive integers by $\mathbb{N}$. Find all functions $f : \mathbb{N} \to \mathbb{N}$ satisfying that for all $m, n \in \mathbb{N}$, $|f(m+n) - f(m)|$ divides $f(n)$.