Proof of a conjecture related to divisibility properties of binomial coefficients

Abstract

Let $a,b$ and $n$ be positive integers with $a>b$. In this note, we prove that $$(2bn+1)(2bn+3)\left(\genfrac{}{}{0ex}{}{2bn}{bn}\right)|3(a-b)(3a-b)(\genfrac{}{}{0ex}{}{2an}{an}\left)\right(\genfrac{}{}{0ex}{}{an}{bn}).$$ This confirms a recent conjecture of Amdeberhan and Moll.

6 pages

References in corpus (1)

• Some divisibility properties of binomial and q-binomial coefficients