A (human) proof of a triple binomial sum supercongruence

TL;DR

This paper proves a specific supercongruence related to a triple binomial sum, confirming a conjecture proposed in a recent study on combinatorial sum congruences.

Contribution

It provides a proof for a particular supercongruence involving triple binomial sums, advancing the understanding of combinatorial sum congruences.

Findings

Proved a supercongruence for a triple binomial sum

Confirmed a conjecture from previous research

Contributed to the theory of combinatorial sum congruences

Abstract

In the recent article arXiv:1606.03351, Apagodu and Zeilberger discuss some applications of an algorithm for finding and proving congruence identities (modulo primes) of indefinite sums of many combinatorial sequence. At the end they propose some supercongruences as conjectures. Here we prove one of them and we leave some remarks for the others.