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Find all real functions withf(x^2 + yf(z)) = xf(x) + zf(y)

Source: INMO 2005 Problem 6

August 23, 2005

functionalgebrafunctional equationalgebra unsolved

Problem Statement

Find all functions

f : \mathbb{R} \longrightarrow \mathbb{R}

such that

f(x^2 + yf(z)) = xf(x) + zf(y) ,

for all

x, y, z \in \mathbb{R}