MEMO 2011 ekipno problem 1


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28. travnja 2012.
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Find all functions f \colon \mathbb R \to \mathbb R such that the equality y^2f(x) + x^2f(y) + xy = xyf(x + y) + x^2 + y^2 holds for all x, y \in \Bbb R, where \Bbb R is the set of real numbers.
Izvor: Srednjoeuropska matematička olimpijada 2011, ekipno natjecanje, problem 1