Question 109
Find all functions $f: \mathbb{Z} \rightarrow \mathbb{Z}$ satisfying
- $f(p) \gt 0$ for all primes $p$,
- $p \mid (f(x)+f(p))^{f(p)}-x$ for all $x \in \mathbb{Z}$ and all primes $p$.
- $f(p) \gt 0$ for all primes $p$,
- $p \mid (f(x)+f(p))^{f(p)}-x$ for all $x \in \mathbb{Z}$ and all primes $p$.