Factors of a perfect square
Volume 163 / 2014
Acta Arithmetica 163 (2014), 141-143
MSC: Primary 11A51; Secondary 11J86.
DOI: 10.4064/aa163-2-4
Abstract
We consider a conjecture of Erdős and Rosenfeld and a conjecture of Ruzsa when the number is a perfect square. In particular, we show that every perfect square $n$ can have at most five divisors between $\sqrt{n} - \sqrt[4]{n}\,(\log n)^{1/7}$ and $\sqrt{n} + \sqrt[4]{n}\,(\log n)^{1/7}$.
