Question 89
Find all functions $f: \mathbb{Z} \rightarrow \mathbb{Z}$ such that:
(i) $f(p)\gt 0$ for every prime number $p$,
(ii) $p \mid (f(x)+f(p))^{f(p)}-x$ for every prime number $p$ and for every $x \in \mathbb{Z}$.
(i) $f(p)\gt 0$ for every prime number $p$,
(ii) $p \mid (f(x)+f(p))^{f(p)}-x$ for every prime number $p$ and for every $x \in \mathbb{Z}$.