Question 87
Find all injective functions $f: \mathbb{N} \rightarrow \mathbb{N}$ such that for all natural numbers $n$
$$
f(f(n)) \leq \frac{f(n)+n}{2}
$$
$$
f(f(n)) \leq \frac{f(n)+n}{2}
$$
MathNet 2009-part-04 — 175 problems (EN–VI) Question 87
Math Olympiad Vault · MathNet 2009-part-04 — 175 problems (EN–VI)