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 ...

IMO 2022 Shortlist A6

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)