Let F be a finite field and |F| = pn, p a prime and n ∈ Z+. For each divisor m of n, prove that F has exactly one subfield E of

Question

Let F be a finite field and |F| = pn, p a prime and n ∈ Z+. For each divisor m of n, prove that F has exactly one subfield E of F such that |E| = pm.

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