MEMO 2015 pojedinačno problem 1


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28. kolovoza 2018.
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Find all surjective functions f : \mathbb{N} \to \mathbb{N} such that for all positive integers a and b, exactly one of the following equations is true: f(a) = f(b), f(a + b) = \min\{f(a), f(b)\}.

Remarks: \mathbb{N} denotes the set of all positive integers. A function f : X \to Y is said to be surjective if for every y \in Y there exists x \in X such that f(x) = y.

Izvor: Srednjoeuropska matematička olimpijada 2015, pojedinačno natjecanje, problem 1