MathDB

shortlisted - function equation

Source: IMO ShortList 2004, algebra problem 6

April 16, 2005

functioncalculusalgebrafunctional equationIMO Shortlist

Problem Statement

Find all functions

f:\mathbb{R} \to \mathbb{R}

satisfying the equation

f(x^2+y^2+2f(xy)) = (f(x+y))^2.

for all

x,y \in \mathbb{R}