IMO 2009 Shortlist A7

Find all functions f from the set of real numbers into the set of real numbers which satisfy for all real x,y the identi...

IMO 2009 Shortlist A7

Category: Algebra

Problem

Find all functions f from the set of real numbers into the set of real numbers which satisfy for all real x,y the identity f(xf(x + y)) = f(yf(x)) + x2 .