1. ## Fields

Let $\displaystyle K$ be a field with $\displaystyle q=p^n$ elements
I want to show that every element $\displaystyle k \in K$ is a solution of $\displaystyle x^q-x=0$
Any hints?

2. K*=K-{0} is a group (under multiplication) of order q-1. Remember Lagrange's theorem?
And what about 0?