Values of the Euler function in various sequences

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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
Pages (from-to)1-19
Number of pages19
JournalMonatshefte fur Mathematik
Issue number1
Publication statusPublished - Sept 2005


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