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Find all real functions

Source: 2012 European Girls’ Mathematical Olympiad P3

April 12, 2012
functionalgebrafunctional equationEGMOEGMO 2012

Problem Statement

Find all functions f:R→Rf:\mathbb{R}\to\mathbb{R} such that f(yf(x+y)+f(x))=4x+2yf(x+y)f\left( {yf(x + y) + f(x)} \right) = 4x + 2yf(x + y) for all x,y∈Rx,y\in\mathbb{R}.
Netherlands (Birgit van Dalen)
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