Two supercongruences involving truncated hypergeometric series

TL;DR

This paper proves two supercongruences related to truncated hypergeometric series, confirming recent conjectures and extending known results using hypergeometric transformations.

Contribution

It establishes two new supercongruences involving truncated hypergeometric series, confirming and extending previous conjectures in the field.

Findings

First supercongruence confirms a recent conjecture.

Second supercongruence partially confirms a conjecture of Guo, Liu, and Schlosser.

Provides a parametric extension of a supercongruence of Long and Ramakrishna.

Abstract

In this paper, we mainly establish two supercongruences involving truncated hypergeometric series by using some hypergeometric transformation formulas. The first supercongruence confirms a recent conjecture of the second author. The second supercongruence confirms a conjecture of Guo, Liu and Schlosser partially, and gives a parametric extension of a supercongruence of Long and Ramakrishna.