Perfect squares have at most five divisors close to its square root

Tsz Ho Chan

Perfect squares have at most five divisors close to its square root

Number Theory 2013-03-11 v1

Authors: Tsz Ho Chan

Abstract

In this paper, we consider a conjecture of Erd\H{o}s and Rosenfeld when the number is a perfect square. In particular, we show that every perfect square $n$ can have at most five divisors between $\sqrt{n} - c \sqrt[4]{n}$ and $\sqrt{n} + c \sqrt[4]{n}$ .

Keywords

perfect square divisors square root Erdős conjecture number theory

Cite

@article{arxiv.1303.2069,
  title  = {Perfect squares have at most five divisors close to its square root},
  author = {Tsz Ho Chan},
  journal= {arXiv preprint arXiv:1303.2069},
  year   = {2013}
}

Comments

4 pages

Related papers

View all related →