JournalscmhVol. 81 , No. 1DOI 10.4171/cmh/40

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

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).