English

On divisors of Lucas and Lehmer numbers

Number Theory 2010-08-10 v1

Abstract

Let u(n) be the n-th term of a Lucas sequence or a Lehmer sequence.In this article we shall establish an estimate from below for the greatest prime factor of u(n) which is of the form nexp(logn/104loglogn). In so doing we are able to resolve a question of Schinzel from 1962 and a conjecture of Erdos from 1965.In addition we are able to give the first general improvement on results of Bang from 1886 and Carmichael from 1912.

Keywords

Cite

@article{arxiv.1008.1274,
  title  = {On divisors of Lucas and Lehmer numbers},
  author = {C. L. Stewart},
  journal= {arXiv preprint arXiv:1008.1274},
  year   = {2010}
}