The <finite field> $K$ is a finite-dimensional <vector space> over its <prime> subfield $F$ of size $p$. A <basis> has some positive length $n$, and every element is uniquely specified by $n$ coefficients in $F$. There are $p$ choices per coefficient, so $\boxed{|K|=p^n}$ and $[K:F]=n$.

Solution

Past exam of the Probability, statistics and options II course of the University of Oxford / 2009 / A / A2 / b / Solution

 Solution (source code)