Question 95
Find all functions $f$ defined on the natural numbers that take values among the natural numbers for which
$$
(f(n))^{p} \equiv n \pmod{f(p)}
$$
for all $n \in \mathbf{N}$ and all prime numbers $p$.
$$
(f(n))^{p} \equiv n \pmod{f(p)}
$$
for all $n \in \mathbf{N}$ and all prime numbers $p$.