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arXiv:1008.1274 [math.NT]AbstractReferencesReviewsResources

On divisors of Lucas and Lehmer numbers

C. L. Stewart

Published 2010-08-06Version 1

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.

Categories: math.NT
Subjects: 11B39, 11J86
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