Problem

Source: 2013 Saudi Arabia IMO TST I p2

Tags: Increasing, function, inequalities, algebra



Let $S = f\{0.1. 2.3,...\}$ be the set of the non-negative integers. Find all strictly increasing functions $f : S \to S$ such that $n + f(f(n)) \le 2f(n)$ for every $n$ in $S$