Question 53
Find all functions $f: \mathbb{N} \rightarrow \mathbb{N}$ such that
$$
f(n+1) \gt \frac{f(n) + f(f(n))}{2}
$$
for all $n \in \mathbb{N}$, where $\mathbb{N}$ is the set of strictly positive integers.
$$
f(n+1) \gt \frac{f(n) + f(f(n))}{2}
$$
for all $n \in \mathbb{N}$, where $\mathbb{N}$ is the set of strictly positive integers.