IMO 2016 Shortlist A4

Denote by R+ the set of all positive real numbers. Find all functions f : R+ → R+ such that xf(x2 )f(f(y)) + f(yf(x)) = ...

imomathematicsolympiadshortlistalgebra

IMO 2016 Shortlist A4

Category: Algebra

Problem

Denote by R+ the set of all positive real numbers. Find all functions f : R+ → R+ such that xf(x2 )f(f(y)) + f(yf(x)) = f(xy) Ä f(f(x2 )) + f(f(y2 )) ä for all positive real numbers x and y.