Smooth squarefree and square-full integers in arithmetic progressions

2018/10/05 by Munsch, Marc, Shparlinski, Igor E., Yau, Kam Hung
#11B25 #11L05 #11L40 #11N25 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1810.02573

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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