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