Open Access
2013 On divisors of Lucas and Lehmer numbers
Cameron L. Stewart
Author Affiliations +
Acta Math. 211(2): 291-314 (2013). DOI: 10.1007/s11511-013-0105-y


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.

Funding Statement

Research supported in part by the Canada Research Chairs Program and by Grant A3528 from the Natural Sciences and Engineering Research Council of Canada.


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Cameron L. Stewart. "On divisors of Lucas and Lehmer numbers." Acta Math. 211 (2) 291 - 314, 2013.


Received: 2 February 2012; Revised: 16 November 2012; Published: 2013
First available in Project Euclid: 31 January 2017

zbMATH: 1362.11070
MathSciNet: MR3143892
Digital Object Identifier: 10.1007/s11511-013-0105-y

Rights: 2013 © Institut Mittag-Leffler

Vol.211 • No. 2 • 2013
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