Let
![\mathbb{Z}_{\geq0}](/media/m/8/c/9/8c9c1a61d19ef7ff9d58a10a701ce93d.png)
be the set of all nonnegative integers. Find all the functions
![f : \mathbb{Z}_{\geq0} \to \mathbb{Z}_{\geq0}](/media/m/9/e/c/9ecbd3134432042e6f34141da0995e03.png)
satisfying the relation
![f(f(f(n))) = f(n + 1) + 1](/media/m/c/1/8/c18dc4bd259d1e3a70f505c0ca422d55.png)
for all
![n \in \mathbb{Z}_{\geq0}](/media/m/b/c/a/bca037bf01bfbfadb2d1f1f811b72a33.png)
.
%V0
Let $\mathbb{Z}_{\geq0}$ be the set of all nonnegative integers. Find all the functions $f : \mathbb{Z}_{\geq0} \to \mathbb{Z}_{\geq0}$ satisfying the relation $$
f(f(f(n))) = f(n + 1) + 1
$$ for all $n \in \mathbb{Z}_{\geq0}$.