On the distribution of consecutive square-free numbers of the form [αn], [αn]+1

2019/03/11 by S. I. Dimitrov, Dimitrov, S. I.
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1903.04545

openalex publication_date 2019/03/11 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

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

Related

• Consecutive square-free values of the form [αp], [αp]+1
• Consecutive square-free numbers of a special form
• Consecutive square-free values for some polynomials
• Pairs of square-free values of the type n²+1, n²+2
• Square-free values of n²+n+1