Proof of a conjecture related to divisibility properties of binomial coefficients

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.

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