Compositions with the euler and carmichael functions | Zendy

William D. Banks | Zendy; Florian Luca | Zendy; Filip Saidak | Zendy; Pantelimon Sta ̆ Nica | Zendy

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Compositions with the euler and carmichael functions

Author(s) -

William D. Banks,

Florian Luca,

Filip Saidak,

Pantelimon Sta ̆ Nica

Publication year - 2005

Publication title -

abhandlungen aus dem mathematischen seminar der universität hamburg

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.354

H-Index - 20

eISSN - 1865-8784

pISSN - 0025-5858

DOI - 10.1007/bf02942044

Subject(s) - euler's formula , order (exchange) , euler number (physics) , euler's totient function , mathematics , function (biology) , combinatorics , arithmetic , discrete mathematics , backward euler method , semi implicit euler method , euler equations , mathematical analysis , biology , business , finance , evolutionary biology

Let ϕ and λ be the Euler and Carmichael functions, respectively. In this paper, we establish lower and upper bounds for the number of positive integers n ≤ x such that ϕ(λ(n)) = λ(ϕ(n)). We also study the normal order of the function ϕ(λ(n))/λ(ϕ(n)).

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