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Stated Fermat’s little theorem.
I expanded this a bit.
“a bit” ;)
I added a redirect from Frobenius automorphism to Frobenius morphism.
I think the correct statement should be: For p a prime, If a finite field has pk elements, then its group of units has pk−pk−1 elements.
I guess essentially the difficulty of proving Fermat’s little theorem is the difficulty of proving that each of 1,2,…,p−1 has an inverse modulo p.
No, Colin. A finite field with pk elements does not refer to the integers modulo pk (which isn’t a field at all). It refers to a degree k algebraic extension of the field with p elements. Up to (non-unique) isomorphism, there is a unique field with pk elements; it is a splitting field for xpk−x∈𝔽p[x].
There is no “difficulty” in proving Fermat’s little theorem.
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