Question 59
Let $\mathbb{P}$ be the set of all prime numbers. Find all functions $f: \mathbb{P} \to \mathbb{P}$ such that
$$
f(p)^{f(q)} + q^p = f(q)^{f(p)} + p^q
$$
holds for all $p, q \in \mathbb{P}$.
$$
f(p)^{f(q)} + q^p = f(q)^{f(p)} + p^q
$$
holds for all $p, q \in \mathbb{P}$.