р 2. Let F be a finite field of characteristic p. (a) Prove that p divides (7) if 0

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р 2. Let F be a finite field of characteristic p. (a) Prove that p divides (7) if 0

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р 2. Let F be a finite field of characteristic p. (a) Prove that p divides (7) if 0 <i<p. (b) Use part (a) to show that o: Fq → Fq defined by o(a) = QP is a ring homomorphism. Conclude that o is injective, therefore surjective, therefore an isomorphism. Hint: Use the binomial theorem. =
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