MK-MO 2008 Problem 1

Find all injective functions $f : \mathbb{N} \to \mathbb{N}$ which satisfy $f(f(n)) \le\frac{n + f(n)}{2}$ for each $n \in \mathbb{N}$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.