MathDB

Do there exist integers m, n and a function f?

Source: International Zhautykov Olympiad 2012 - D2 - P1

January 31, 2012

functioninductionnumber theory proposednumber theory

Problem Statement

Do there exist integers

m, n

and a function

f\colon \mathbb R \to \mathbb R

satisfying simultaneously the following two conditions?

\bullet

f(f(x))=2f(x)-x-2

for any

x \in \mathbb R

;

\bullet

ii)

m \leq n

and

f(m)=n