English

On the digital representation of integers with bounded prime factors

Number Theory 2016-09-27 v1

Abstract

Let b2b \ge 2 be an integer. Not much is known on the representation in base bb of prime numbers or of numbers whose prime factors belong to a given, finite set. Among other results, we establish that any sufficiently large integer which is not a multiple of bb and has only small (in a suitable sense) prime factors has at least four nonzero digits in its representation in base bb.

Keywords

Cite

@article{arxiv.1609.07926,
  title  = {On the digital representation of integers with bounded prime factors},
  author = {Yann Bugeaud},
  journal= {arXiv preprint arXiv:1609.07926},
  year   = {2016}
}