# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1702.07232