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arXiv · 1810.02573

Smooth squarefree and square-full integers in arithmetic progressions

Marc Munsch·Igor E. Shparlinski·Kam Hung Yau
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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 $p$.

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Marc Munsch, Igor E. Shparlinski, Kam Hung Yau. 2018-10-05. Smooth squarefree and square-full integers in arithmetic progressions. https://arxiv.org/abs/1810.02573

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