IMO 2018 Shortlist A1

Let Qą0 denote the set of all positive rational numbers. Determine all fun tions f : Qą0 Ñ Qą0 satisfying f x2 fpyq2 ˘ “...

imomathematicsolympiadshortlistalgebra

IMO 2018 Shortlist A1

Category: Algebra

Problem

Let Qą0 denote the set of all positive rational numbers. Determine all fun tions f : Qą0 Ñ Qą0 satisfying f ` x2 fpyq2 ˘ “ fpxq2 fpyq for all x,y P Qą0. (Switzerland)