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2015 IMO Problems/Problem 5

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Let $\mathbb{R}$ be the set of real numbers. Determine all functions $f$:$\mathbb{R}\rightarrow\mathbb{R}$ satisfying the equation $f(x+f(x+y))+f(xy) = x+f(x+y)+yf(x)$ for all real numbers $x$ and $y$.

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