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arXiv · 1008.1274

On divisors of Lucas and Lehmer numbers

C. L. Stewart
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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.

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C. L. Stewart. 2010-08-06. On divisors of Lucas and Lehmer numbers. https://arxiv.org/abs/1008.1274

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