New congruences on multiple harmonic sums and Bernoulli numbers

被引：0

作者：

Wang, Liuquan ^{[1
]}

机构：

[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China

来源：

PUBLICATIONES MATHEMATICAE-DEBRECEN | 2020年 / 97卷 / 1-2期

基金：

中国国家自然科学基金;

关键词：

congruences; Bernoulli numbers; multiple harmonic sums; CURIOUS CONGRUENCE;

D O I：

10.5486/PMD.2020.8768

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let P-n denote the set of positive integers which are prime to n. Let B-n be the n-th Bernoulli number. For any prime p >= 11 and integer r >= 2, we prove that Sigma(l1+l2+ ... +l6 = pr l1, ... ,l6 is an element of Pp) 1/l(1)l(2)l(3)l(4)l(5)l(6) - 5!/18p(r-1) B-p-3(2) (mod p(r)). This extends a family of curious congruences. We also obtain other interesting congruences involving multiple harmonic sums and Bernoulli numbers.

引用

页码：161 / 180

页数：20

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