= Solution
The <characteristic of a field> is the least positive <integer> $r$ with $r1_K=0$, or zero if none exists. In a <finite field> a positive such <integer> exists because the sequence $0,1_K,2\cdot1_K,\ldots$ must repeat.
The <prime field>[prime subfield] is the <intersection> of all subfields of $K$, equivalently the <subfield> generated by $1_K$. In characteristic $p$ it is the copy of $\mathbb F_p$ formed by the multiples of $1_K$. Every <field automorphism> preserves $1_K$ and addition, so it fixes every element of this <subfield>.
Finally, once the order-$n$ <Frobenius automorphism> below is established, all its $n$ powers are distinct. Any automorphism fixes $F$ and is determined by its value at the generator $\lambda$. That value must be a root of the degree-$n$ <minimal polynomial> of $\lambda$, so there are at most $n$ automorphisms. Hence
$$
\boxed{\operatorname{Aut}(K)=\langle\vartheta\rangle\cong C_n}.
$$
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