Let $K$ be a field of $p$ elements.
Let $f(x) \in K [x]$ be an irreducible polynomial of degree $n$.
Prove that the field $K[x]/(f(x))$ has $p^n$ elements.
By given theorem, let $K$ be a field, $P(x)\in K[x]$ an irreducible polynomial. Then $\exists$ a field $F$ s.t. $P(x)$ has a root in $F$, then $K \subseteq F$.
Below are some notes that may can get me the proof.
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