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
Školjka