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Asian Pacific Mathematical Olympiad 2010 Problem 5

Source:

May 7, 2010
functionalgebra proposedalgebra

Problem Statement

Find all functions ff from the set R\mathbb{R} of real numbers into R\mathbb{R} which satisfy for all x,y,z∈Rx, y, z \in \mathbb{R} the identity f(f(x)+f(y)+f(z))=f(f(x)−f(y))+f(2xy+f(z))+2f(xz−yz).f(f(x)+f(y)+f(z))=f(f(x)-f(y))+f(2xy+f(z))+2f(xz-yz).
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