Geodesic
Proof of a conjecture of Amdeberhan and Moll on a divisibility property of binomial coefficients
Quan-Hui Yang1
1Nanjing University of Information Science and Technology
The electronic journal of combinatorics, Tome 22 (2015) no. 1
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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.
DOI : 10.37236/4104
Classification : 05A10, 11B65
Mots-clés : binomial coefficients, \(p\)-adic order, divisibility properties

Quan-Hui Yang  1

1 Nanjing University of Information Science and Technology 
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     author = {Quan-Hui Yang},
     title = {Proof of a conjecture of {Amdeberhan} and {Moll} on a divisibility property of binomial coefficients},
     journal = {The electronic journal of combinatorics},
     year = {2015},
     volume = {22},
     number = {1},
     doi = {10.37236/4104},
     zbl = {1305.05005},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/4104/}
}
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Quan-Hui Yang. Proof of a conjecture of Amdeberhan and Moll on a divisibility property of binomial coefficients. The electronic journal of combinatorics, Tome 22 (2015) no. 1. doi: 10.37236/4104

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