Let K be nonempty corps , K^∗ =K−{0_K } Prove that 1) Π_(x∈K^∗ ) x = −1 2)Deduce that p is prime ⇔ (p−1)!≡−1[p]


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Question Number 146073 by savitar last updated on 10/Jul/21
$Let K be nonempty corps , K^∗ =K−{0_K } Prove that 1) Π_(x∈K^∗ ) x = −1 2)Deduce that p is prime ⇔ (p−1)!≡−1[p]$
$L e t K b e n o n e m p t y c o r p s, K^{} = K - {0_{K}}$ $P r o v e t h a t$ $1) \prod_{x \in K^{}} x = - 1$ $2) D e d u c e t h a t$ $p i s p r i m e \Leftrightarrow (p - 1)! \equiv - 1 [p]$
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