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TH-TMO 2016 Problem 3

    Determine all functions f:R→Rf : R \to R satisfying f(f(x)f(y)+f(y)f(z)+f(z)f(x))=f(x)+f(y)+f(z)f (f(x)f(y) + f(y)f(z) + f(z)f(x))= f(x) + f(y) + f(z) for all real numbers x,y,zx, y, z .

    Dataset text AI-MO AoPS. Quoted with source.

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