TY - JOUR

T1 - Some divisibility properties of the Euler function

AU - Banks, William D.

AU - Luca, Florian

AU - Shparlinski, Igor E.

N1 - Copyright 2005 Cambridge University Press. Article originally published in Glasgow Mathematical Journal, Vol. 47, Issue 3, pp. 517-528. The original article can be found at http://dx.doi.org/10.1017/S0017089505002752.

PY - 2005/9

Y1 - 2005/9

N2 - Let $\varphi(\cdot)$ denote the Euler function, and let a > 1 be a fixed integer. We study several divisibility conditions which exhibit typographical similarity with the standard formulation of the Euler theorem, such as an ≡ 1 (mod φ(n)), and we estimate the number of positive integers $n\le x$ satisfying these conditions.

AB - Let $\varphi(\cdot)$ denote the Euler function, and let a > 1 be a fixed integer. We study several divisibility conditions which exhibit typographical similarity with the standard formulation of the Euler theorem, such as an ≡ 1 (mod φ(n)), and we estimate the number of positive integers $n\le x$ satisfying these conditions.

UR - http://www.scopus.com/inward/record.url?scp=28244486830&partnerID=8YFLogxK

U2 - 10.1017/S0017089505002752

DO - 10.1017/S0017089505002752

M3 - Article

AN - SCOPUS:28244486830

VL - 47

SP - 517

EP - 528

JO - Glasgow Mathematical Journal

JF - Glasgow Mathematical Journal

SN - 0017-0895

IS - 3

ER -