On divisors of Lucas and Lehmer numbers

@article{Stewart2010OnDO,
  title={On divisors of Lucas and Lehmer numbers},
  author={C. L. Stewart},
  journal={Acta Mathematica},
  year={2010},
  volume={211},
  pages={291-314}
}
Let un be the nth 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 un 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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