Question 83
Let $\mathbb{Z}_{\geqslant 0}$ be the set of all nonnegative integers. Find all the functions $f: \mathbb{Z}_{\geqslant 0} \rightarrow \mathbb{Z}_{\geqslant 0}$ satisfying the relation
$$
f(f(f(n)))=f(n+1)+1
$$
for all $n \in \mathbb{Z}_{\geqslant 0}$.
$$
f(f(f(n)))=f(n+1)+1
$$
for all $n \in \mathbb{Z}_{\geqslant 0}$.