Some supercongruences of arbitrary length

TL;DR

This paper proves supercongruences modulo p^2 for truncated hypergeometric series with specific parameters, extending understanding of hypergeometric supercongruences for arbitrary lengths.

Contribution

It establishes new supercongruences for hypergeometric series with parameters involving multiple copies of 1/2 and 1, generalizing previous results to arbitrary lengths.

Findings

Proves supercongruences modulo p^2 for specific hypergeometric series

Extends supercongruence results to arbitrary series length d≥2

Provides new identities for truncated hypergeometric series

Abstract

We prove supercongruences modulo $p^2$ for values of truncated hypergeometric series at some special points. The parameters of the hypergeometric series are $d$ copies of $1/2$ and $d$ copies of $1$ for any integer $d\ge2$.