Problem

Source: Macedonian Mathematical Olympiad 2019

Tags: Macedonia, functions, number theory, 2019



Determine all functions $f: \mathbb {N} \to \mathbb {N}$ such that $n!\hspace{1mm} +\hspace{1mm} f(m)!\hspace{1mm} |\hspace{1mm} f(n)!\hspace{1mm} +\hspace{1mm} f(m!)$, for all $m$, $n$ $\in$ $\mathbb{N}$.