Hello.

I have to proof the following proposition:

Let $\displaystyle K$ be a finite field. Then $\displaystyle K$ has $\displaystyle q=p^n$ elements, whereas $\displaystyle p$ is the characteristic of $\displaystyle K$ and $\displaystyle n=[K:\mathbb{F}_p]$.

Furthermore I have to proof, that $\displaystyle x^q = x$ for all $\displaystyle x \in K$.

Could anybody of you explain, how to proof the proposition?

Bye,

Lisa