IMO 2010 Shortlist A5

Denote by Q the set of all positive rational numbers. Determine all functions f : Q ÑQ which satisfy the following equat...

imomathematicsolympiadshortlistalgebra

IMO 2010 Shortlist A5

Category: Algebra

Problem

Denote by Q the set of all positive rational numbers. Determine all functions f : Q ÑQ which satisfy the following equation for all x,y PQ : f fpxq2 y  x3 fpxyq. (1) (Switzerland)