IMO 2023 Shortlist N8
Let Zą0 be the set of positive integers. Determine all functions f : Zą0 Ñ Zą0 such that fbfpaq pa 1q “ pa 1qfpbq holds ...
Category: Number Theory
Problem
Let Zą0 be the set of positive integers. Determine all functions f : Zą0 Ñ Zą0 such
that
fbfpaq
pa 1q “ pa 1qfpbq
holds for all a,b P Zą0, where fk
pnq “ fpfp¨¨¨fpnq¨¨¨qq denotes the composition of f with
itself k times.
(Taiwan) 10 Chiba, Japan, 2nd–13th July 2023 Shortlisted problems – solutions 11