IMO 2024 Shortlist N7
Let Zą0 denote the set of positive integers. Let f : Zą0 Ñ Zą0 be a function satisfying the following property: for m, n...
Category: Number Theory
Problem
Let Zą0 denote the set of positive integers. Let f : Zą0 Ñ Zą0 be a function satisfying the following property: for m, n P Zą0, the equation fpmnq2 “ fpm2 qfpfpnqqfpmfpnqq holds if and only if m and n are coprime. For each positive integer n, determine all the possible values of fpnq. (Japan) 10 Bath, United Kingdom, 10th –22nd July 2024 Shortlisted problems – solutions 11