Proof of a supercongruence via the Wilf–Zeilberger method

In this paper, we prove a supercongruence via the Wilf–Zeilberger method and symbolic summation algorithms in the setting of difference rings. That is, for any prime p>3,∑n=0(p−1)/23n+1(−8)n(2nn)3≡p(−1p)+p34(2p)Ep−3(14)(modp4), where (⋅p) stands for the Legendre symbol, and En(x) are the Euler po...

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Bibliographic Details
Published inJournal of symbolic computation Vol. 107; pp. 269 - 278
Main Author Mao, Guo-Shuai
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.11.2021
Subjects
Binomial coefficients
Euler polynomials
Supercongruence
Wilf–Zeilberger method
11A07
33F10
Binomial coefficients
Euler polynomials
11B65
11B68
Wilf–Zeilberger method
Supercongruence
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Summary:In this paper, we prove a supercongruence via the Wilf–Zeilberger method and symbolic summation algorithms in the setting of difference rings. That is, for any prime p>3,∑n=0(p−1)/23n+1(−8)n(2nn)3≡p(−1p)+p34(2p)Ep−3(14)(modp4), where (⋅p) stands for the Legendre symbol, and En(x) are the Euler polynomials. This confirms a special case of a recent conjecture of Z.-W. Sun (Sun, 2019, (2.18)).
ISSN:0747-7171
1095-855X
DOI:10.1016/j.jsc.2021.04.001