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Research Article | Open Access

New q-supercongruences arising from a summation of basic hypergeometric series

Chuanan Wei1,2,3, Chun Li2,3( )
School of Biomedical Information and Engineering, Hainan Medical University, Haikou, China
Key Laboratory of Data Science and Intelligence Education of Ministry of Education, Hainan Normal University, Haikou, China
School of Mathematics and Statistics, Hainan Normal University, Haikou, China
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Abstract

With the help of a summation of basic hypergeometric series, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials, we prove some new q-supercongruences on sums of q-shifted factorials. Especially, we give a q-analogue of a formula due to Liu [14].

Keywords

q-supercongruencebasic hypergeometric seriescreative microscoping methodChinese remainder theorem for coprime polynomials
CLC number: 11A07, 11B65, 33D15

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AIMS Mathematics
Volume 7 Issue 3,
March 2022
Pages 4125-4136
DOI: 10.3934/math.2022228

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Cite this article:
Wei C, Li C. New q-supercongruences arising from a summation of basic hypergeometric series. AIMS Mathematics, 2022, 7(3): 4125-4136. https://doi.org/10.3934/math.2022228

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Received: 20 August 2021
Revised: 28 November 2021
Accepted: 07 December 2021
Published: 15 March 2021
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)