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A q-SUPERCONGRUENCE ARISING FROM ANDREWS’ $_4\phi _3$ IDENTITY

Part of: Sequences and sets Basic hypergeometric functions Elementary number theory

Published online by Cambridge University Press:  29 August 2024

JI-CAI LIU Open the ORCID record for JI-CAI LIU [Opens in a new window]  and
JING LIU
JI-CAI LIU*
Affiliation:
Department of Mathematics, Wenzhou University, Wenzhou 325035, PR China
JING LIU
Affiliation:
Department of Mathematics, Wenzhou University, Wenzhou 325035, PR China e-mail: 22451025009@stu.wzu.edu.cn
*
e-mail: jcliu2016@gmail.com
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Abstract

We establish a q-analogue of a supercongruence related to a supercongruence of Rodriguez-Villegas, which extends a q-congruence of Guo and Zeng [‘Some q-analogues of supercongruences of Rodriguez-Villegas’, J. Number Theory 145 (2014), 301–316]. The important ingredients in the proof include Andrews’ $_4\phi _3$ terminating identity.

Keywords

q-congruenceAndrews’ 4ϕ3 identitycyclotomic polynomial

MSC classification

Primary: 11B65: Binomial coefficients; factorials; $q$-identities
Secondary: 11A07: Congruences; primitive roots; residue systems 33D15: Basic hypergeometric functions in one variable, $_rphi_s$

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 111 , Issue 2 , April 2025 , pp. 223 - 227
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The first author was supported by the National Natural Science Foundation of China (grant no. 12171370).

References

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