Arithmetic properties of φ(n)/λ(n) and the structure of the multiplicative group modulo n

Igor E. Shparlinski; William D Banks; Florian Luca

doi:10.4171/cmh/40

JournalscmhVol. 81, No. 1pp. 1–22

Arithmetic properties of φ(n)/λ(n) and the structure of the multiplicative group modulo n

Igor E. Shparlinski
University of New South Wales, Sydney, Australia
William D Banks
University of Missouri-Columbia, United States
Florian Luca
UNAM, Campus Morelia, Michoacán, Mexico

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Abstract

For a positive integer $n$ , we let $φ (n)$ and $λ (n)$ denote the Euler function and the Carmichael function, respectively. We define $ξ (n)$ as the ratio $φ (n) / λ (n)$ and study various arithmetic properties of $ξ (n)$ .

Cite this article

Igor E. Shparlinski, William D Banks, Florian Luca, Arithmetic properties of φ(n)/λ(n) and the structure of the multiplicative group modulo n. Comment. Math. Helv. 81 (2006), no. 1, pp. 1–22

DOI 10.4171/CMH/40