MathDB

{f(f(x))=x+1, f: &Zeta;->&Zeta;

Source: 1991 Greece MO Grade XII p1

September 6, 2024

functionalgebrafunctional

Problem Statement

Prove that there is no function

f: \mathbb{Z}\to\mathbb{Z}

such that

f(f(x))=x+1

, for all

x\in\mathbb{Z}