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<p>In this paper, we consider the existence of infinitely many consecutive cube-free numbers in Piatetski-Shapiro sequences. We prove that, for any fixed <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1351_Article_IEq5.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="70" /> </InlineMediaObject> <EquationSource Format="TEX">\(1&lt;c&lt;2\)</EquationSource> </InlineEquation>, there exist infinitely many consecutive cube-free integers in Piatetski-Shapiro sequences.</p>

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On consecutive cube-free numbers of the form \(\lfloor n^c\rfloor\), \(\lfloor n^c\rfloor\)+1

  • 期刊论文

  • 发表日期：

    2025年8月5日

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  • Pinthira Tangsupphathawat,
  • Teerapat Srichan

摘要

In this paper, we consider the existence of infinitely many consecutive cube-free numbers in Piatetski-Shapiro sequences. We prove that, for any fixed \(1<c<2\) , there exist infinitely many consecutive cube-free integers in Piatetski-Shapiro sequences.