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(Solved): 21. Prove that the Frobenius map :GF(pn)GF(pn) given by :p is an automorphism of orde ...

$21. Prove that the Frobenius map \( \Phi: \operatorname{GF}\left(p^{n}\right) \rightarrow \operatorname{GF}\left(p^{n}\right)$

21. Prove that the Frobenius map

? : GF (p^{n}) ? GF (p^{n})

given by

? : ? ? ?^{p}

is an automorphism of order

n

.

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