MathDB
smo 2019 open 2nd round q2

Source:

August 15, 2019
functional equationfunctionalgebra

Problem Statement

find all functions f:ZZf : \mathbb{Z} \to \mathbb{Z} such that
f(f(x)f(y))=1xyf(-f(x)-f(y)) = 1-x-y   \forall x,y \in \mathbb{Z}