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

  • Quan-Hui Yang
Keywords: binomial coefficients, p-adic order, divisibility properties

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.
Published
2015-01-09
Article Number
P1.9