Proof of a Conjecture of Amdeberhan and Moll on a Divisibility Property of Binomial Coefficients

Quan-Hui Yang

Abstract


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.

Keywords


binomial coefficients; p-adic order; divisibility properties

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