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

[1]

Bailey WN., 1935, GEN HYPERGEOMETRIC S

[2] On some congruences of certain binomial sums [J].

Chen, Yungui ;

Xie, Xiaoyan ;

He, Bing .

RAMANUJAN JOURNAL, 2016, 40 (02) :237-244

[3] Finding identities with the WZ method [J].

Gessel, IM .

JOURNAL OF SYMBOLIC COMPUTATION, 1995, 20 (5-6) :537-566

[4] "DIVERGENT" RAMANUJAN-TYPE SUPERCONGRUENCES [J].

Guillera, Jesus ;

Zudilin, Wadim .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 140 (03) :765-777

[5] Some q-congruences on double basic hypergeometric sums [J].

Guo, Victor J. W. ;

Lian, Xiuguo .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2021, 27 (03) :453-461

[6] SOME CONGRUENCES ON TRUNCATED HYPERGEOMETRIC SERIES [J].

He, Bing .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 143 (12) :5173-5180

[7]

Hu D.-W., 2017, PhD thesis

[8] On congruences involving Bernoulli numbers and the quotients of Fermat and Wilson [J].

Lehmer, E .

ANNALS OF MATHEMATICS, 1938, 39 :350-360

[9] Some supercongruences occurring in truncated hypergeometric series [J].

Long, Ling ;

Ramakrishna, Ravi .

ADVANCES IN MATHEMATICS, 2016, 290 :773-808

[10] HYPERGEOMETRIC EVALUATION IDENTITIES AND SUPERCONGRUENCES [J].

Long, Ling .

PACIFIC JOURNAL OF MATHEMATICS, 2011, 249 (02) :405-418

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