MathDB

RMM 2013 Problem 2

Source:

March 2, 2013

functionfloor functioninductionalgebra unsolvedfunctional equation

Problem Statement

Does there exist a pair

(g,h)

of functions

g,h:\mathbb{R}\rightarrow\mathbb{R}

such that the only function

f:\mathbb{R}\rightarrow\mathbb{R}

satisfying

f(g(x))=g(f(x))

and

f(h(x))=h(f(x))

for all

x\in\mathbb{R}

is identity function

f(x)\equiv x