English

Smooth squarefree and square-full integers in arithmetic progressions

Number Theory 2019-03-11 v2

Abstract

We obtain new lower bounds on the number of smooth squarefree integers up to xx in residue classes modulo a prime pp, relatively large compared to xx, which in some ranges of pp and xx improve that of A. Balog and C. Pomerance (1992). We also estimate the smallest squarefull number in almost all residue classes modulo a prime pp.

Keywords

Cite

@article{arxiv.1810.02573,
  title  = {Smooth squarefree and square-full integers in arithmetic progressions},
  author = {Marc Munsch and Igor E. Shparlinski and Kam Hung Yau},
  journal= {arXiv preprint arXiv:1810.02573},
  year   = {2019}
}
R2 v1 2026-06-23T04:29:23.736Z