MEMO 2015 ekipno problem 2


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28. kolovoza 2018.
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Determine all functions f : \mathbb{R}\backslash \{0\} \to \mathbb{R}\backslash \{0\} such that f(x^2yf(x)) + f(1) = x^2f(x) + f(y) holds for all nonzero real numbers x and y.

Izvor: Srednjoeuropska matematička olimpijada 2015, ekipno natjecanje, problem 2