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Slippery functional equation

Source: European Mathematical Cup 2022, Senior Division, Problem 3

December 20, 2022
functionfunctional equationsubstitutionsCauchy functional equationalgebra

Problem Statement

Determine all functions f:Rā†’Rf: \mathbb{R} \to \mathbb{R} such that f(x3)+f(y)3+f(z)3=3xyz f(x^3) + f(y)^3 + f(z)^3 = 3xyz for all real numbers xx, yy and zz with x+y+z=0x+y+z=0.
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