Proof of some congruences via the hypergeometric identities

被引：0

作者：

Mao, Guo-Shuai ^{[1
]}

机构：

[1] Nanjing Univ Informat Sci & Technol, Dept Math, Nanjing 210044, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2024年 / 540卷 / 02期

关键词：

Congruences; Central binomial coefficients; Hypergeometric identities; Harmonic numbers; p-Adic Gamma function; BERNOULLI NUMBERS; SUPERCONGRUENCE;

D O I：

10.1016/j.jmaa.2024.128651

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, via the hypergeometric identities of 3 F 2 , 4 F 3 and 5 F 4 , we prove some congruences involving cubes of central binomial coefficients and harmonic numbers. We also obtained a congruence which generalizes a conjecture of Long, this conjecture has been confirmed by Swisher (Res. Math. Sci. 2:18, 2015). (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页数：14

共 30 条

[21] Congruences concerning Bernoulli numbers and Bernoulli polynomials [J].

Sun, ZH .

DISCRETE APPLIED MATHEMATICS, 2000, 105 (1-3) :193-223

[22]

Sun ZH, 2022, Arxiv, DOI arXiv:2210.17255

[23] Congruences concerning Legendre polynomials II [J].

Sun, Zhi-Hong .

JOURNAL OF NUMBER THEORY, 2013, 133 (06) :1950-1976

[24] Congruences involving Bernoulli and Euler numbers [J].

Sun, Zhi-Hong .

JOURNAL OF NUMBER THEORY, 2008, 128 (02) :280-312

[25]

Sun ZW, 2022, Arxiv, DOI arXiv:2210.07238

[26] A REFINEMENT OF A CONGRUENCE RESULT BY VAN HAMME AND MORTENSON [J].

Sun, Zhi-Wei .

ILLINOIS JOURNAL OF MATHEMATICS, 2012, 56 (03) :967-979

[27] On the supercongruence conjectures of van Hamme [J].

Swisher, Holly .

RESEARCH IN THE MATHEMATICAL SCIENCES, 2015, 2 (01)

[28] Supercongruences related to 3F2(1) involving harmonic numbers [J].

Tauraso, Roberto .

INTERNATIONAL JOURNAL OF NUMBER THEORY, 2018, 14 (04) :1093-1109

[29] Supercongruences concerning truncated hypergeometric series [J].

Wang, Chen ;

Pan, Hao .

MATHEMATISCHE ZEITSCHRIFT, 2022, 300 (01) :161-177

[30] ON CONGRUENCES FOR BINOMIAL COEFFICIENTS [J].

YEUNG, KM .

JOURNAL OF NUMBER THEORY, 1989, 33 (01) :1-17

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