MEMO 2018 pojedinačno problem 1


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8. rujna 2018.
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Let \mathbb{Q}^+ denote the set of all positive rational numbers and let \alpha \in \mathbb{Q}^+. Determine all functions f : \mathbb{Q}^+ \rightarrow (\alpha, +\infty) such that f\bigg(\frac{x+y}{\alpha}\bigg) = \frac{f(x)+f(y)}{\alpha} for all x, y \in \mathbb{Q}^+

Izvor: Srednjoeuropska matematička olimpijada 2016, pojedinačno natjecanje, problem 1