Problem

Source: ELMO 2022 P6

Tags: functional equation, algebra, ELMO 2022



Find all functions $f\colon \mathbb{Z} \rightarrow \mathbb{Z}$ such that, for all integers $m$ and $n$,$$f(f(m)-n)+f(f(n)-m)=f(m+n).$$ Espen Slettnes and Luke Robitaille