- Acta Math.
- Volume 211, Number 2 (2013), 315-382.
p-adic logarithmic forms and a problem of Erdős
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 (see Erdős ) and its far-reaching generalization to Lucas and Lehmer numbers. In the present paper the author delivers three refinements upon Yu  required by C. L. Stewart for solving completely the problem of Erdős (see Stewart ). 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.
Acta Math., Volume 211, Number 2 (2013), 315-382.
Received: 3 June 2011
Revised: 8 November 2012
First available in Project Euclid: 31 January 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11J86: Linear forms in logarithms; Baker's method
Secondary: 11B39: Fibonacci and Lucas numbers and polynomials and generalizations
2013 © Institut Mittag-Leffler
Yu, Kunrui. p -adic logarithmic forms and a problem of Erdős. Acta Math. 211 (2013), no. 2, 315--382. doi:10.1007/s11511-013-0106-x. https://projecteuclid.org/euclid.acta/1485892740