The Explicit Formula and Parity for Some Generalized Euler Functions

Shichun Yang; Qunying Liao; Shan Du; Huili Wang

The Explicit Formula and Parity for Some Generalized Euler Functions

Number Theory 2021-12-24 v2

Authors: Shichun Yang , Qunying Liao , Shan Du , Huili Wang

Abstract

Based on elementary methods and techniques, the explicit formula for the generalized Euler function $\varphi_{e}(n)(e=8,12)$ is given, and then a sufficient and necessary condition for $\varphi_{8}(n)$ or $\varphi_{12}(n)$ to be odd is obtained, respectively.

Cite

@article{arxiv.2112.11725,
  title  = {The Explicit Formula and Parity for Some Generalized Euler Functions},
  author = {Shichun Yang and Qunying Liao and Shan Du and Huili Wang},
  journal= {arXiv preprint arXiv:2112.11725},
  year   = {2021}
}

Comments

19pages,2 figures

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