MathNet 2023-part-05 — 191 problems (EN–VI) Question 47

Find the strictly increasing functions $f : \mathbb{N} \to \mathbb{N}$ with the following property: the number $f(x) \cdot f(y)$ divides the number $(1+2x) \cdot f(y) + (1+2y) \cdot f(x)$, for any natural numbers $x$ and $y$.