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April 11th, 2019, 08:34 AM   #1
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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.
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April 11th, 2019, 03:43 PM   #2
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Quote:
(gcd (n, m) / n) (C (n, m))
Clarify statement.
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April 11th, 2019, 03:53 PM   #3
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See this article. The hint was presumably referring to Bézout's identity (also called Bézout's lemma) rather than Bézout's theorem.
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April 11th, 2019, 06:52 PM   #4
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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.
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April 11th, 2019, 07:38 PM   #5
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Thank you skipjack
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