José María GRAU¹, Florian LUCA², Antonio M. OLLER-MARCÉN³

1. Departmento de Matemáticas, Universidad de Oviedo, Avda. Calvo Sotelo s/n, C. P. 33007, Oviedo, Spain; 2. Instituto de Matemáticas, Universidad Nacional Autónoma de México, C. P. 58089, Morelia, Michoacán, México and The John Knopfmacher Centre for Applicable Analysis and Number Theory, University of the Witwatersrand, P. O. Wits 2050, South Africa; 3. Centro Universitario de la Defensa, Academia General Militar, Ctra. Huesca s/n, C. P. 50090, Zaragoza, Spain

Abstract：In this paper, we characterize the odd positive integers n satisfying the congruence  （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.

Key words：Congruence; Giuga numbers; asymptotic density

Source：Acta Mathematica Sinica, English Series.2012, 28(4)