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On two functions arising in the study of the Euler and Carmichael quotients

Volume 149 / 2017

Florian Luca, Min Sha, Igor E. Shparlinski Colloquium Mathematicum 149 (2017), 179-192 MSC: 11A25, 11K65, 11N36. DOI: 10.4064/cm6910-3-2017 Published online: 8 May 2017

Abstract

We investigate two arithmetic functions naturally occurring in the study of the Euler and Carmichael quotients. The functions are related to the frequency of vanishing of the Euler and Carmichael quotients. We obtain several results concerning the relations between these functions as well as their typical and extreme values.

Authors

  • Florian LucaSchool of Mathematics
    University of the Witwatersrand
    Private Bag X3
    Wits 2050, South Africa
    and
    Department of Mathematics
    Faculty of Sciences
    University of Ostrava
    30. dubna 22
    701 03 Ostrava 1, Czech Republic
    e-mail
  • Min ShaSchool of Mathematics and Statistics
    University of New South Wales
    Sydney, NSW 2052, Australia
    e-mail
  • Igor E. ShparlinskiSchool of Mathematics and Statistics
    University of New South Wales
    Sydney, NSW 2052, Australia
    e-mail

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