MathDB

6

Part of 2021 Switzerland - Final Round

Problems(1)

Irritated function

Source: Switzerland Final Round 2021 P6

2/24/2021
Let N\mathbb{N} be the set of positive integers. Let f:N→Nf: \mathbb{N} \rightarrow \mathbb{N} be a function such that for every positive integer n∈Nn \in \mathbb{N} f(n) -n<2021   \text{and}   f^{f(n)}(n) =n Prove that f(n)=nf(n)=n for infinitely many n∈Nn \in \mathbb{N}
functionalgebranice problem