Problem

Source: Moldova TST 2022

Tags: function, algebra, functional equation



The function $f:\mathbb{N} \rightarrow \mathbb{N}$ verifies: $1) f(n+2)-2022 \cdot f(n+1)+2021 \cdot f(n)=0, \forall n \in \mathbb{N};$ $2) f(20^{22})=f(22^{20});$ $3) f(2021)=2022$. Find all possible values of $f(2022)$.