On the 3-adic Valuation of a Cubic Binomial Sum

TL;DR

This paper proves a conjecture regarding the 3-adic valuation of a specific cubic binomial sum, advancing understanding in number theory related to p-adic valuations and binomial coefficients.

Contribution

It provides a proof of a recent conjecture on the 3-adic valuation of a cubic binomial sum, contributing to the field of p-adic number theory.

Findings

Confirmed the conjecture on 3-adic valuation

Established new properties of cubic binomial sums

Enhanced understanding of p-adic valuations in combinatorial contexts

Abstract

In this short note, we prove a conjecture recently posed by Alekseyev, Amdeberhan, Shallit, and Vukusic on the 3-adic valuation of a cubic binomial sum.