Let $p$ be a prime number and $F$ a field of $p^{23}$ elements. Let $\phi : F \longrightarrow F$ be the field automorphism of $F$ sending $a$ to $a^p$. Let $K := \{ a \in F \mid \phi(a) = a \}$. What is the value of $[K : \mathbb{F}_p]$?
Let $p$ be a prime number and $F$ a field of $p^{23}$ elements. Let $\phi : F \longrightarrow F$ be the field automorphism of $F$ sending $a$ to $a^p$. Let $K := \{ a \in F \mid \phi(a) = a \}$. What is the value of $[K : \mathbb{F}_p]$?