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BALKAN-SL 2021 A6

Find all functions f:R→Rf: \mathbb{R} \rightarrow \mathbb{R} such that

f(xy)=f(x)f(y)+f(f(x+y))f(x y)=f(x) f(y)+f(f(x+y))

holds for all x,y∈Rx, y \in \mathbb{R}.

Dataset text NuminaMath olympiads. Quoted with source.

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