On the Lehmer's totient problem on Number Fields

Konstantinos Smpokos

On the Lehmer's totient problem on Number Fields

Number Theory 2020-09-01 v2

Authors: Konstantinos Smpokos

Abstract

Lehmer's totient problem asks if there exists a composite number $d$ such that its totient divide $d-1$ . In this article we generalize the Lehmer's totient problem in algebraic number fields. We introduce the notion of a Lehmer number. Lehmer numbers are defined to be the natural numbers which obey the Lehmer's problem in the ring of algebraic integers of a number field.

Keywords

fields

Cite

@article{arxiv.2007.02318,
  title  = {On the Lehmer's totient problem on Number Fields},
  author = {Konstantinos Smpokos},
  journal= {arXiv preprint arXiv:2007.02318},
  year   = {2020}
}

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11 Pages

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