p-adic logarithmic forms and a problem of Erdos

• 成果类型: Article
• 署名作者: Yu, Kunrui
• 署名单位: Hong Kong University of Science & Technology
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-013-0106-x
• 发表日期: 2013
• 页码: 315-382
• 关键词: rational linear form; lucas; divisors; fibonacci; numbers; fermat

摘要

For any natural number m(> 1) let P(m) denote the greatest prime divisor of m. By the problem of ErdAs in the title of the present paper we mean the general version of his problem, that is, his conjecture from 1965 that (see ErdAs [10]) and its far-reaching generalization to Lucas and Lehmer numbers. In the present paper the author delivers three refinements upon Yu [40] required by C. L. Stewart for solving completely the problem of ErdAs (see Stewart [25]). The author gives also some remarks on the solution of this problem, aiming to be more streamlined with respect to the p-adic theory of logarithmic forms.