English

Consecutive square-free numbers of a special form

Number Theory 2018-05-28 v3

Abstract

In the present paper we prove that for any fixed 1<c<7/61<c<7/6 there exist infinitely many consecutive square-free numbers of the form [nc],[nc]+1[n^c], [n^c]+1 and we also establish an asymptotic formula in given interval.

Keywords

Cite

@article{arxiv.1702.03983,
  title  = {Consecutive square-free numbers of a special form},
  author = {S. I. Dimitrov},
  journal= {arXiv preprint arXiv:1702.03983},
  year   = {2018}
}