continuing what you've already done: 0 and 1 are in K. also if then so also if then so

defined by is a ring homomorphism and thus contains a field hence can be considered as a finite dimensional vector space over

2.) Show that any finite field has order p^n, where p is prime.

I have that Char F = p and the order of a divides p, and I know that the order of a is either 1 or p. I also know that p divides the order of the field, so F must contain an element of order p. I'm just having trouble connecting that to proving any finite field has order p^n.

Any help would be greatly appreciated. Thanks.

let then because