$p$-adic logarithmic forms and a problem of Erdős

Kunrui Yu Department of Mathematics, Hong Kong University of Science and Technology

Number Theory mathscidoc:1701.24003

Acta Mathematica, 211, (2), 315-382, 2011.6
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 $$\frac{P(2^n-1)}{n} \to \infty \quad {\rm as}\, n \to \infty$$ (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.
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@inproceedings{kunrui2011$p$-adic,
  title={$p$-adic logarithmic forms and a problem of Erdős},
  author={Kunrui Yu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203402084766782},
  booktitle={Acta Mathematica},
  volume={211},
  number={2},
  pages={315-382},
  year={2011},
}
Kunrui Yu. $p$-adic logarithmic forms and a problem of Erdős. 2011. Vol. 211. In Acta Mathematica. pp.315-382. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203402084766782.
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