Let-K-be-nonempty-corps-K-K-0-K-Prove-that-1-x-K-x-1-2-Deduce-that-p-is-prime-p-1-1-p-

Question Number 146073 by savitar last updated on 10/Jul/21

L e t K b e n o n e m p t y c o r p s, K^{*} = K - {0_{K}}

P r o v e t h a t

1) \prod_{x \in K^{*}} x = - 1

2) D e d u c e t h a t

p i s p r i m e \Leftrightarrow (p - 1)! \equiv - 1 [p]