A recursion formula for the generalized Euler function $ \varphi_e(n) $

Canze Zhu; Qunying Liao

A recursion formula for the generalized Euler function $ \varphi_e(n) $

Number Theory 2022-08-26 v2

Authors: Canze Zhu , Qunying Liao

Abstract

In this paper, basing on the linear algebra methods and elementary techniques, for any positive integers $e$ and $n$ , we obtain a recursion formula for the generalized Euler function $\varphi_e(n)$ , which is determined by some matrices related to a congruence equation modulo $e$ . Furthermore, through the recursion formula, we get the explicit formula for $\varphi_5(n)$ . Our results generalize the corresponding results in \cite{A4,A8,A10,A11}.

Keywords

special functions and series expansions

Cite

@article{arxiv.2105.10870,
  title  = {A recursion formula for the generalized Euler function $ \varphi_e(n) $},
  author = {Canze Zhu and Qunying Liao},
  journal= {arXiv preprint arXiv:2105.10870},
  year   = {2022}
}

Comments

There are some mistakes in the Manuscript

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