IMO 2022 Shortlist A6
Let R be the set of real numbers. We denote by F the set of all functions f : R Ñ R such that fpx fpyqq “ fpxq fpyq for ...
Category: Algebra
Problem
Let R be the set of real numbers. We denote by F the set of all functions f : R Ñ R
such that
fpx fpyqq “ fpxq fpyq
for every x,y P R. Find all rational numbers q such that for every function f P F, there exists
some z P R satisfying fpzq “ qz.
(Indonesia)