Solutions of the congruence 1+2f (n) + . . . + nf (n) ≡ 0 (mod n)

被引：4

作者：

Maria Grau, Jose ^{[1
]}

Moree, Pieter ^{[2
]}

Oller-Marcen, Antonio M. ^{[3
]}

机构：

[1] Univ Oviedo, Dept Matemat, Avda Calvo Sotelo S-N, Oviedo 33007, Spain

[2] Max Planck Inst Math, Vivatsgasse 7, D-53111 Bonn, Germany

[3] Ctr Univ Def Zaragoza, Ctra Huesca S-N, Zaragoza 50090, Spain

来源：

MATHEMATISCHE NACHRICHTEN | 2016年 / 289卷 / 07期

关键词：

Power sums; congruence; divisibility; asymptotic density; Giuga numbers;

D O I：

10.1002/mana.201500057

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we characterize, in terms of the prime divisors of n, the pairs (k, n) for which n divides Sigma(n)(j=1) j(k). As an application, we derive some results on the sets M-f := {n >= 1 : f (n) > 1 and Sigma(n)(j=1) j(f (n)) equivalent to 0 (mod n)} for some choices of f. C (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：820 / 830

页数：11

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