English

On equations $\sigma(n)=\sigma(n+k)$ and $\varphi(n)=\varphi(n+k)$

Number Theory 2018-10-18 v2

Abstract

We study the distribution of solutions of equations σ(n)=σ(n+k)\sigma(n)=\sigma(n+k) and φ(n)=φ(n+k)\varphi(n)=\varphi(n+k). We give new upper bounds for these solutions.

Keywords

Cite

@article{arxiv.1001.2511,
  title  = {On equations $\sigma(n)=\sigma(n+k)$ and $\varphi(n)=\varphi(n+k)$},
  author = {Tomohiro Yamada},
  journal= {arXiv preprint arXiv:1001.2511},
  year   = {2018}
}

Comments

9 pages, the author's final version