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Finding almost squares IV |
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| Authors: | Tsz Ho Chan |
| Institution: | (1) Department of Mathematical Sciences, University of Memphis, Memphis, TN, 38152, U.S.A. |
| Abstract: | In this paper, we continue the study of almost squares; these are integers n representable as n = a · b for some ![$$a, b \in 1,3\sqrt{n}]$$](/content/j78710l1638t307l/13_2009_Article_3058_TeX2GIFIEq1.gif) . We show that almost all (in the measure–theoretic sense) short intervals x, x + (log x)12] contain at least one almost square, and we consider related questions. Moreover, a result of Erdős shows that the exponent
12 cannot be smaller than 0.086 ....
Received: 26 June 2008; Revised: 22 December 2008 |
| Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) Primary 11N25 11M06 Secondary 11B75 |
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