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On a variant of Giuga numbers |
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| Authors: | José María Grau Florian Luca Antonio M. Oller-Marcén |
| Affiliation: | [1]Departmento de Matemdticas, Universidad de Oviedo, Avda. Calvo Sotelo s/n, C. P. 33007, Oviedo, Spain [2]Instituto de Matemdticas, Universidad Nacional AutSnoma de Mdxico, C. P. 58089, Morelia, Michoacdn, Mdxico [3]The John Knopfmacher Centre for Applicable Analysis and Number Theory, University of the Witwatersrand, P. O. Wits 2050, South Africa |
| Abstract: | In this paper, we characterize the odd positive integers n satisfying the congruence $sumnolimits_{j = 1}^{n - 1} {j^{tfrac{{n - 1}} {2}} } equiv 0 (mod n)$sumnolimits_{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 |
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