Consecutive square-free values of the form $\mathbf{[αp], [αp]+1}$

S. I. Dimitrov

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arXiv · 1907.03721

Consecutive square-free values of the form $\mathbf{[αp], [αp]+1}$

S. I. Dimitrov

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Abstract

In this short paper we shall prove that there exist infinitely many consecutive square-free numbers of the form $[αp]$, $[αp]+1$, where $p$ is prime and $α>0$ is irrational algebraic number. We also establish an asymptotic formula for the number of such square-free pairs when $p$ does not exceed given sufficiently large positive integer.

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BibTeX RIS

S. I. Dimitrov. 2019-07-03. Consecutive square-free values of the form $\mathbf{[αp], [αp]+1}$. https://arxiv.org/abs/1907.03721

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