Supercongruences between truncated ${}_3F_2$ hypergeometric series

TL;DR

This paper proves four new supercongruences involving truncated hypergeometric series and p-adic Gamma functions, extending known results in the field of number theory.

Contribution

It introduces four novel supercongruences between truncated ${}_3F_2$ hypergeometric series, expanding the class of known supercongruences.

Findings

Established four supercongruences involving hypergeometric series

Extended Rodriguez-Villegas supercongruences

Connected hypergeometric series with p-adic Gamma functions

Abstract

We establish four supercongruences between truncated ${}_3F_2$ hypergeometric series involving $p$-adic Gamma functions, which extend some of the Rodriguez-Villegas supercongruences.