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Factors of a perfect square

Volume 163 / 2014

Tsz Ho Chan Acta Arithmetica 163 (2014), 141-143 MSC: Primary 11A51; Secondary 11J86. DOI: 10.4064/aa163-2-4


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 $\sqrt{n} + \sqrt[4]{n}\,(\log n)^{1/7}$.


  • Tsz Ho ChanDepartment of Arts and Sciences
    Victory University
    255 N. Highland Street
    Memphis, TN 38111, U.S.A.

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