English

Each positive rational number has the form $\varphi(m^2)/\varphi(n^2)$

History and Overview 2020-10-23 v2 Number Theory

Abstract

In this note, we show that each positive rational number can be written as φ(m2)/φ(n2)\varphi(m^2)/\varphi(n^2), where φ\varphi is Euler's totient function and mm and nn are positive integers.

Cite

@article{arxiv.2001.03736,
  title  = {Each positive rational number has the form $\varphi(m^2)/\varphi(n^2)$},
  author = {Dmitry Krachun and Zhi-Wei Sun},
  journal= {arXiv preprint arXiv:2001.03736},
  year   = {2020}
}

Comments

3 pages

R2 v1 2026-06-23T13:08:35.634Z