Question 94
Find all pairs $p, q$ of distinct primes, sets $D \subseteq \mathbb{R}$ and functions $f: D \to D$ fulfilling
$$
f^p(x) = x^p \quad \text{and} \quad f^q(x) = x^q
$$
for all $x \in D$. (Here, $f^n$ denotes the $n$'th iterate of $f$.)
$$
f^p(x) = x^p \quad \text{and} \quad f^q(x) = x^q
$$
for all $x \in D$. (Here, $f^n$ denotes the $n$'th iterate of $f$.)