I was wondering if x^p = 1 implies that x =1 in a finite field of characteristic p, or in other words

If x^p = 1 (mod p), does that imply that x = 1 (mod p) ?

If so why?

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- Aug 31st 2008, 07:30 AMpetersmithSolution of x^p = 1 in a finite field of char p
I was wondering if x^p = 1 implies that x =1 in a finite field of characteristic p, or in other words

If x^p = 1 (mod p), does that imply that x = 1 (mod p) ?

If so why? - Aug 31st 2008, 07:38 AMMoo
- Aug 31st 2008, 08:25 AMThePerfectHacker
If then .

Thus if .

Quote:

Originally Posted by**Moo**

However, a finite field need not be a the integers modulo .

Thus, it does not cover all the cases.

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