Problem

Source: Saudi Arabia IMO TST Day I Problem 4

Tags: function, induction, algebra unsolved, algebra



Find all functions $f:\mathbb{N}\rightarrow\mathbb{N}$ such that \[f(n+1)>\frac{f(n)+f(f(n))}{2}\] for all $n\in\mathbb{N}$, where $\mathbb{N}$ is the set of strictly positive integers.