Sums of reciprocals modulo composite integers

被引：4

作者：

Cosgrave, John B. ^{[1
]}

Dilcher, Karl ^{[1
]}

机构：

[1] Dalhousie Univ, Dept Math & Stat, Halifax, NS B3H 3J5, Canada

来源：

JOURNAL OF NUMBER THEORY | 2013年 / 133卷 / 11期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Lehmer's congruences; Fermat quotients; Euler quotients; Bernoulli numbers; Bernoulli polynomials; CONGRUENCES INVOLVING BERNOULLI; QUOTIENTS; FERMAT; EULER; GAUSS;

D O I：

10.1016/j.jnt.2013.04.016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In 1938, as part of a wider study, Emma Lehmer derived a set of four related congruences for certain sums of reciprocals over various ranges, modulo squares of odd primes. These were recently extended to congruences modulo squares of positive integers n, with certain restrictions on n. In this paper we characterize those excluded n for which the congruences still hold, and find the correct reduced moduli in the cases in which the congruences do not hold. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：3565 / 3577

页数：13

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