JournalscmhVol. 81, No. 1pp. 1–22

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

  • 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
Arithmetic properties of <em>φ(n)/λ(n)</em> and the structure of the multiplicative group modulo <em>n</em> cover
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Abstract

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

Cite this article

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

DOI 10.4171/CMH/40