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Acta Mathematica Sinica, English Series

, Volume 28, Issue 4, pp 653–660 | Cite as

On a variant of Giuga numbers

  • José María Grau
  • Florian Luca
  • Antonio M. Oller-Marcén
Article

Abstract

In this paper, we characterize the odd positive integers n satisfying the congruence \(\sum\nolimits_{j = 1}^{n - 1} {j^{\tfrac{{n - 1}} {2}} } \equiv 0 (mod n)\). We show that the set of such positive integers has an asymptotic density which turns out to be slightly larger than 3/8.

Keywords

Congruence Giuga numbers asymptotic density 

MR(2000) Subject Classification

11A07 11B05 

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • José María Grau
    • 1
  • Florian Luca
    • 2
    • 3
  • Antonio M. Oller-Marcén
    • 4
  1. 1.Departmento de MatemáticasUniversidad de OviedoOviedoSpain
  2. 2.Instituto de MatemáticasUniversidad Nacional Autónoma de MéxicoMorelia, MichoacánMéxico
  3. 3.The John Knopfmacher Centre for Applicable Analysis and Number TheoryUniversity of the WitwatersrandJohannesburgSouth Africa
  4. 4.Centro Universitario de la DefensaAcademia General MilitarZaragozaSpain

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