MathDB

IMO Shortlist 2013, Algebra #5

Source: IMO Shortlist 2013, Algebra #5

July 9, 2014

functionalgebrafunctional equationIMO Shortlist

Problem Statement

Let

\mathbb{Z}_{\ge 0}

be the set of all nonnegative integers. Find all the functions

f: \mathbb{Z}_{\ge 0} \rightarrow \mathbb{Z}_{\ge 0}

satisfying the relation

f(f(f(n))) = f(n+1 ) +1

for all

n\in \mathbb{Z}_{\ge 0}