Proof of some conjectural congruences modulo p3

被引：7

作者：

Mao, Guo-Shuai ^{[1
]}

Li, Danrui ^{[1
]}

机构：

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

来源：

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2022年 / 28卷 / 04期

关键词：

Congruences; Apery-like numbers; harmonic numbers; Euler numbers; BERNOULLI;

D O I：

10.1080/10236198.2022.2046739

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we mainly prove the following conjectures of Z.-H. Sun [New congruences involving Apery-like numbers, preprint (2020). Available at arXiv:2004.07172v2]: Let p > 3 be a prime. Then G(2p) G(2) + 3072(-1)((p-1)/2)p(2)E(p-3) (mod p(3)), G(2p-1) (-1)((p-1)/2)16(4(p-1))G(1) + 164p(2)E(p-3) (mod p(3)), G(3p) G(3) + 94464(-1)(p-1/2) p(2)E(p-3) (mod p(3)). where G(n) = Sigma(n)(k=0) (2k k)(2) (2n-2k n-k)4(n-k), and E-n stands for the nth Euler number.

引用

页码：496 / 509

页数：14