For what positive integers $k$ there exists a function $f : N \to N$ such that for all $n \in N$ we have $\underbrace{\hbox{f(f(... f(n)....))}}_{\hbox{k times}} = f(n) + 2$ ?
Source:
Tags: functional equation, 5th edition
For what positive integers $k$ there exists a function $f : N \to N$ such that for all $n \in N$ we have $\underbrace{\hbox{f(f(... f(n)....))}}_{\hbox{k times}} = f(n) + 2$ ?