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) ?
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?
x cannot be =0, otherwise, it wouldn't be possible that x^p=1
Considering that x is an element of the field, , we have by Fermat's little theorem :
So if , then ...
Hmmm I think it killed the question... or I've made a mistake ^^'