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Functional equation

Source: APMO 2002

April 8, 2006
functioninductionalgebra unsolvedalgebra

Problem Statement

Let R{\bf R} denote the set of all real numbers. Find all functions ff from R{\bf R} to R{\bf R} satisfying: (i) there are only finitely many ss in R{\bf R} such that f(s)=0f(s)=0, and (ii) f(x4+y)=x3f(x)+f(f(y))f(x^4+y)=x^3f(x)+f(f(y)) for all x,yx,y in R{\bf R}.
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