From c09c3c86b5eab6f16a67fdd9b70618741e0c1727 Mon Sep 17 00:00:00 2001
From: thery
Date: Wed, 10 Jul 2019 14:28:34 +0200
Subject: totient for prime

---
 mathcomp/ssreflect/prime.v | 3 +++
 1 file changed, 3 insertions(+)

(limited to 'mathcomp')

diff --git a/mathcomp/ssreflect/prime.v b/mathcomp/ssreflect/prime.v
index 16e44e2..7d07293 100644
--- a/mathcomp/ssreflect/prime.v
+++ b/mathcomp/ssreflect/prime.v
@@ -1338,6 +1338,9 @@ move=> p_pr e_gt0; rewrite totientE ?expn_gt0 ?prime_gt0 //.
 by rewrite primes_exp // primes_prime // unlock /= muln1 pfactorK.
 Qed.
 
+Lemma totient_prime p : prime p -> totient p = p.-1.
+Proof. by move=> p_prime; rewrite -{1}[p]expn1 totient_pfactor // muln1. Qed.
+
 Lemma totient_coprime m n :
   coprime m n -> totient (m * n) = totient m * totient n.
 Proof.
-- 
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