Proof of a conjecture of Amdeberhan and Moll on a divisibility property of binomial coefficients (Q490309)
From MaRDI portal
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Proof of a conjecture of Amdeberhan and Moll on a divisibility property of binomial coefficients |
scientific article |
Statements
Proof of a conjecture of Amdeberhan and Moll on a divisibility property of binomial coefficients (English)
0 references
22 January 2015
0 references
Summary: Let \(a,b\) and \(n\) be positive integers with \(a>b\). In this note, we prove that \[ (2bn+1)(2bn+3){2bn \choose bn}\bigg|3(a-b)(3a-b){2an \choose an}{an\choose bn}. \] This confirms a recent conjecture of Amdeberhan and Moll.
0 references
binomial coefficients
0 references
\(p\)-adic order
0 references
divisibility properties
0 references
0 references
