PROOF OF A CONGRUENCE FOR HARMONIC NUMBERS CONJECTURED BY Z.-W. SUN

被引：6

作者：

Mestrovic, Romeo ^{[1
]}

机构：

[1] Univ Montenegro, Dept Math, Maritime Fac, Kotor 85330, Montenegro

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2012年 / 8卷 / 04期

关键词：

Harmonic numbers; congruences; Bernoulli numbers; WOLSTENHOLMES THEOREM; SUMS;

D O I：

10.1142/S1793042112500649

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a positive integer n let H-n = Sigma(n)(k=1) 1/k be the nth harmonic number. In this paper, we prove that for any prime p >= 7, Sigma(p-1)(k=1) H-k(2)/k(2) equivalent to 4/5pB(p-5) (mod p(2)), which confirms the conjecture recently proposed by Z.-W. Sun. Furthermore, we also prove two similar congruences modulo p(2).

引用

页码：1081 / 1085

页数：5

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