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JP Journal of Algebra, Number Theory and Applications

JP Journal of Algebra, Number Theory and Applications
Volume 40, Issue 6, Pages 945 - 956 (December 2018)
http://dx.doi.org/10.17654/NT040060945

CONSECUTIVE SQUARE-FREE NUMBERS OF THE FORM [n^c], [n^c] + 1

S. I. Dimitrov

Abstract:

In the present paper we show that for any fixed 1 < c < 22/13 there exist infinitely many consecutive square-free numbers of the form [n^c], [n^c] + 1.

Keywords and phrases:

square-free numbers, asymptotic formula.

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