olymmath

NMC 1998 Problem 1

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Determine all functions ff defined in the set of rational numbers and taking their values in the same set such that the equation f(x+y)+f(x−y)=2f(x)+2f(y)f(x+y)+f(x-y)=2 f(x)+2 f(y) holds for all rational numbers xx and yy.

Dataset text NuminaMath olympiads. Quoted with source.

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f(x)=a x^{2}

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