Values of the Euler function in various sequences

William D. Banks, Kevin Ford, Florian Luca, Francesco Pappalardi, Igor E. Shparlinski

Research output: Contribution to journalArticlepeer-review

Abstract

Let φ(n) and λ(n) denote the Euler and Carmichael functions, respectively. In this paper, we investigate the equation φ(n) r = λ(n) s , where r ≥ s ≥ 1 are fixed positive integers. We also study those positive integers n, not equal to a prime or twice a prime, such that φ(n) = p - 1 holds with some prime p, as well as those positive integers n such that the equation φ(n) = f(m) holds with some integer m, where f is a fixed polynomial with integer coefficients and degree degf > 1.

Original languageEnglish (US)
Pages (from-to)1-19
Number of pages19
JournalMonatshefte fur Mathematik
Volume146
Issue number1
DOIs
StatePublished - Sep 2005

Keywords

  • Carmichael function
  • Euler function
  • Polynomials
  • Primes

ASJC Scopus subject areas

  • Mathematics(all)

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