MathDB

integer valued functions with at most two values for f(2022)

Source: Macedonian TST 2022, P3

May 21, 2022

algebrafunctionfunctional equation

Problem Statement

We consider all functions

f: \mathbb{N} \rightarrow \mathbb{N}

such that

f(f(n)+n)=n

and

f(a+b-1) \leq f(a)+f(b)

for all positive integers

a, b, n

. Prove that there are at most two values for

f(2022)

\textit {Proposed by Ilija Jovcheski}