On divisors of Lucas and Lehmer numbers

Cameron L. Stewart Department of Pure Mathematics, University of Waterloo

Number Theory mathscidoc:1701.24002

Acta Mathematica, 211, (2), 291-314, 2012.2
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$n$exp(log$n$/104 log log$n$). In doing so, we are able to resolve a question of Schinzel from 1962 and a conjecture of Erdős from 1965. In addition we are able to give the first general improvement on results of Bang from 1886 and Carmichael from 1912.
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  title={On divisors of Lucas and Lehmer numbers},
  author={Cameron L. Stewart},
  booktitle={Acta Mathematica},
Cameron L. Stewart. On divisors of Lucas and Lehmer numbers. 2012. Vol. 211. In Acta Mathematica. pp.291-314. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203401980570781.
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