MathDB

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

.
Proposed by Žymantas Darbėnas (Zymantas Darbenas), Lithuania

Problem Statement