Smooth squarefree and square-full integers in arithmetic progressions

Marc Munsch, Igor E. Shparlinski, Kam Hung Yau

Research output: Contribution to journalArticle

Abstract

We obtain new lower bounds on the number of smooth squarefree integers up to $x$ in residue classes modulo a prime $p$, relatively large compared to $x$, which in some ranges of $p$ and $x$ improve that of A. Balog and C. Pomerance (1992). We also estimate the smallest squarefull number in almost all residue classes modulo a prime $p$.
Original languageEnglish
Pages (from-to) 56-70
JournalMathematika
Volume66
Issue number1
DOIs
Publication statusPublished - Jan 2020

Keywords

  • math.NT
  • 11N25, 11B25, 11L05, 11L40

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