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Found problems: 1

2008 IMO Shortlist, 6
Tags: range , functional equation , function , algebra
Let $ f: \mathbb{R}\to\mathbb{N}$ be a function which satisfies $ f\left(x \plus{} \dfrac{1}{f(y)}\right) \equal{} f\left(y \plus{} \dfrac{1}{f(x)}\right)$ for all $ x$, $ y\in\mathbb{R}$. Prove that there is a positive integer which is not a value of $ f$. [i]Proposed by Žymantas Darbėnas (Zymantas Darbenas), Lithuania[/i]