IMO Shortlist 2010 problem A6
Dodao/la:
arhiva23. lipnja 2013. Suppose that

and

are two functions defined on the set of positive integers and taking positive integer values. Suppose also that the equations

and

hold for all positive integers. Prove that

for all positive integer

Proposed by Alex Schreiber, Germany
%V0
Suppose that $f$ and $g$ are two functions defined on the set of positive integers and taking positive integer values. Suppose also that the equations $f(g(n)) = f(n) + 1$ and $g(f(n)) = g(n) + 1$ hold for all positive integers. Prove that $f(n) = g(n)$ for all positive integer $n.$
Proposed by Alex Schreiber, Germany
Izvor: Međunarodna matematička olimpijada, shortlist 2010