On divisors of Lucas and Lehmer numbers

• 成果类型: Article
• 署名作者: Stewart, Cameron L.
• 署名单位: University of Waterloo
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-013-0105-y
• 发表日期: 2013
• 页码: 291-314
• 关键词: adic logarithmic forms; primitive divisors; fibonacci; fermat; distance

摘要

Let u (n) 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 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 ErdAs from 1965. In addition we are able to give the first general improvement on results of Bang from 1886 and Carmichael from 1912.