Two supercongruences involving truncated hypergeometric series

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.