Find all unbounded functions $f:\mathbb Z \rightarrow \mathbb Z$ , such that $f(f(x)-y)|x-f(y)$ holds for any integers $x,y$.
Problem
Source: ISR 2021 February TST p.2
Tags: functional equation, functional equation in Z, algebra
Source: ISR 2021 February TST p.2
Tags: functional equation, functional equation in Z, algebra
Find all unbounded functions $f:\mathbb Z \rightarrow \mathbb Z$ , such that $f(f(x)-y)|x-f(y)$ holds for any integers $x,y$.