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Prove that the functional equations are equivalent

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September 15, 2010
algebrafunctional equationIMO ShortlistIMO 1979

Problem Statement

Prove that the functional equations f(x+y)=f(x)+f(y),f(x + y) = f(x) + f(y), \text{and} \qquad f(x + y + xy) = f(x) + f(y) + f(xy)   (x, y \in \mathbb R) are equivalent.
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