Covering an arithmetic progression with geometric progressions and vice versa

Carlo Sanna

doi:10.1142/S1793042114500456

Covering an arithmetic progression with geometric progressions and vice versa

Number Theory 2014-09-18 v1

Authors: Carlo Sanna

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Abstract

We show that there exists a positive constant C such that the following holds: Given an infinite arithmetic progression A of real numbers and a sufficiently large integer n (depending on A), there needs at least Cn geometric progressions to cover the first n terms of A. A similar result is presented, with the role of arithmetic and geometric progressions reversed.

Keywords

arithmetic progressions number theory collatz conjecture

Cite

@article{arxiv.1311.4331,
  title  = {Covering an arithmetic progression with geometric progressions and vice versa},
  author = {Carlo Sanna},
  journal= {arXiv preprint arXiv:1311.4331},
  year   = {2014}
}