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2013 p-adic logarithmic forms and a problem of Erdős
Kunrui Yu
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Acta Math. 211(2): 315-382 (2013). DOI: 10.1007/s11511-013-0106-x


For any natural number m(>1) let P(m) denote the greatest prime divisor of m. By the problem of Erdős in the title of the present paper we mean the general version of his problem, that is, his conjecture from 1965 that P(2n-1)nasn(see Erdős [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 Erdős (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.


Dedicated to Prof. Gisbert Wüstholz on the occasion of his 61st birthday.


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Kunrui Yu. "p-adic logarithmic forms and a problem of Erdős." Acta Math. 211 (2) 315 - 382, 2013.


Received: 3 June 2011; Revised: 8 November 2012; Published: 2013
First available in Project Euclid: 31 January 2017

zbMATH: 1362.11071
MathSciNet: MR3143893
Digital Object Identifier: 10.1007/s11511-013-0106-x

Primary: 11J86
Secondary: 11B39

Rights: 2013 © Institut Mittag-Leffler

Vol.211 • No. 2 • 2013
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