Problem 4 Determine all functions f:N→Nf: \mathbb {N} \to \mathbb {N}f:N→N such that n!+f(m)!∣f(n)!+f(m!)n!\hspace{1mm} +\hspace{1mm} f(m)!\hspace{1mm} |\hspace{1mm} f(n)!\hspace{1mm} +\hspace{1mm} f(m!)n!+f(m)!∣f(n)!+f(m!) , for all mmm , nnn ∈\in∈ N\mathbb{N}N .