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On the distribution of consecutive square-free numbers of the form $\mathbf{[αn], [αn]+1}$

Published 11 Mar 2019 in math.NT | (1903.04545v2)

Abstract: In the present paper we show that there exist infinitely many consecutive square-free numbers of the form $[\alpha n]$, $[\alpha n]+1$, where $\alpha>1$ is irrational number with bounded partial quotient or irrational algebraic number.

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Authors (1)

  1. S. I. Dimitrov 

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