A $p$-adic supercongruence for truncated hypergeometric series ${}_7F_6$

TL;DR

This paper proves a new $p$-adic supercongruence for truncated hypergeometric series ${}_7F_6$ using identities and properties of the $p$-adic Gamma function, extending recent results and confirming a conjecture.

Contribution

It introduces a novel $p$-adic supercongruence for ${}_7F_6$ hypergeometric series, advancing the understanding of supercongruences in number theory.

Findings

Established a $p$-adic supercongruence for ${}_7F_6$ series

Derived related supercongruences extending recent results

Confirmed a supercongruence conjecture

Abstract

Using an identity due to Gessel and Stanton and some properties of the $p$-adic Gamma function, we establish a $p$-adic supercongruence for truncated hypergeometric series ${}_7F_6$. From it we deduce some related supercongruences, which extend certain recent results and confirm a supercongruence conjecture.