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
收藏
页码：820 / 830
页数：11
相关论文
共 50 条
  • [21] On symmetric digraphs of the congruence xk ≡ y (mod n)
    Somer, Lawrence
    Krizek, Michal
    DISCRETE MATHEMATICS, 2009, 309 (08) : 1999 - 2009
  • [22] CONGRUENCES SIGMA (N) = A (MOD N) AND N = A (MOD PHI (N))
    POMERANC.C
    NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 21 (01): : A51 - A51
  • [23] Primes of the form x2 + dy2 with x 0(mod N) or y O (mod N)
    Dukkipati, Ambedkar
    Palimar, Sushma
    PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2017, 127 (01): : 35 - 43
  • [24] STRENGTH OF N-F BONDS IN NF3 AND OF N-F AND N-N BONDS IN N2F4
    KENNEDY, A
    COLBURN, CB
    JOURNAL OF CHEMICAL PHYSICS, 1961, 35 (05): : 1892 - &
  • [25] Numeric solutions of congruence u(p-1)-1 0 (mod p(2))
    Haussner, R
    JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1927, 156 (1/4): : 223 - 226
  • [26] On the Analytic Solutions of the Functional Equations w 1 f(a 1 z) plus w 2 f(a 2 z) plus ... plus w n f(a n z)=0
    Matias Sepulcre, Juan
    Vidal, Tomas
    MEDITERRANEAN JOURNAL OF MATHEMATICS, 2015, 12 (03) : 667 - 678
  • [27] 关于图C_n2,C_n3(n≡0（mod5）)与图C_n3(n≡0（mod7）)的全染色
    强会英
    西北师范大学学报(自然科学版), 2006, (01) : 27 - 28
  • [28] N BARYONS(S=0,I=1/2)p,N~+=uud;n,N~0=udd
    K.A.Olive
    K.Agashe
    C.Amsler
    M.Antonelli
    J.-F.Arguin
    D.M.Asner
    H.Baer
    H.R.Band
    R.M.Barnett
    T.Basaglia
    C.W.Bauer
    J.J.Beatty
    V.I.Belousov
    J.Beringer
    G.Bernardi
    S.Bethke
    H.Bichsel
    O.Biebe
    E.Blucher
    S.Blusk
    G.Brooijmans
    O.Buchmueller
    V.Burkert
    M.A.Bychkov
    R.N.Cahn
    M.Carena
    A.Ceccucci
    A.Cerr
    D.Chakraborty
    M.-C.Chen
    R.S.Chivukula
    K.Copic
    G.Cowan
    O.Dahl
    G.D’Ambrosio
    T.Damour
    D.de Florian
    A.de Gouvea
    T.DeGrand
    P.de Jong
    G.Dissertor
    B.A.Dobrescu
    M.Doser
    M.Drees
    H.K.Dreiner
    D.A.Edwards
    S.Eidelman
    J.Erler
    V.V.Ezhela
    W.Fetscher
    Chinese Physics C, 2014, (09) : 1371 - 1427
  • [29] AN EFFICIENT SOLUTION OF THE CONGRUENCE X2+KY2=M(MOD N)
    POLLARD, JM
    SCHNORR, CP
    IEEE TRANSACTIONS ON INFORMATION THEORY, 1987, 33 (05) : 702 - 709
  • [30] 关于同余式2≡1（mod n）
    袁平之
    科学通报 , 1988, (05) : 396
12345