IMO 2024 Shortlist A7
Let Q be the set of rational numbers. Let f : Q Ñ Q be a function such that the following property holds: for all x, y P...
Category: Algebra
Problem
Let Q be the set of rational numbers. Let f : Q Ñ Q be a function such that the
following property holds: for all x, y P Q,
fpx fpyqq “ fpxq y or fpfpxq yq “ x fpyq.
Determine the maximum possible number of elements of tfpxq ` fp´xq | x P Qu.
(Japan) 4 Bath, United Kingdom, 10th
–22nd
July 2024