Problem

Source: X International Festival of Young Mathematicians Sozopol 2019, Theme for 10-12 grade

Tags: functional equation, number theory



Does there exist a strictly increasing function $f:\mathbb{N}\rightarrow \mathbb{N}$, such that for $\forall$ $n\in \mathbb{N}$: $f(f(f(n)))=n+2f(n)$?