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arXiv · 1903.04545

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

S. I. Dimitrov
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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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S. I. Dimitrov. 2019-03-11. On the distribution of consecutive square-free numbers of the form $\mathbf{[\alpha n], [\alpha n]+1}$. https://arxiv.org/abs/1903.04545

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