My Math Forum Problem (Bezout's theorem/GCD)

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 April 11th, 2019, 08:34 AM #1 Newbie   Joined: Apr 2019 From: canada Posts: 3 Thanks: 0 Problem (Bezout's theorem/GCD) Hello, can you help me solve this problem? It's urgent please: Let 1 <= m <= n be two integers. Note by C (n; m) = (n!) / ((n-m)! m!) Show that (gcd (n, m) / n) (C (n, m)) is an integer. Tip: Bézout's theorem. Thank you. Last edited by skipjack; April 11th, 2019 at 03:56 PM.
April 11th, 2019, 03:43 PM   #2
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Quote:
 (gcd (n, m) / n) (C (n, m))
Clarify statement.

 April 11th, 2019, 03:53 PM #3 Global Moderator   Joined: Dec 2006 Posts: 20,757 Thanks: 2138 See this article. The hint was presumably referring to Bézout's identity (also called Bézout's lemma) rather than Bézout's theorem.
 April 11th, 2019, 06:52 PM #4 Newbie   Joined: Apr 2019 From: canada Posts: 3 Thanks: 0 It's actually called théorème de Bézout in French. I maybe translated it wrong; sorry. Last edited by skipjack; April 12th, 2019 at 05:31 AM.
 April 11th, 2019, 07:38 PM #5 Newbie   Joined: Apr 2019 From: canada Posts: 3 Thanks: 0 Thank you skipjack

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