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On the digital representation of smooth numbers

Published online by Cambridge University Press:  29 August 2017

YANN BUGEAUD  and
HAJIME KANEKO
YANN BUGEAUD
Affiliation:
Institut de Recherche Mathématique Avancée, U.M.R. 7501, Université de Strasbourg et C.N.R.S., 7, rue René Descartes, 67084 Strasbourg, France. e-mail: bugeaud@math.unistra.fr
HAJIME KANEKO
Affiliation:
Institute of Mathematics, University of Tsukuba, 1-1-1, Tennodai, Tsukuba, Ibaraki, 305-8571, Japan. Center for Integrated Research in Fundamental Science and Engineering (CiRfSE), University of Tsukuba, 1-1-1, Tennodai, Tsukuba, Ibaraki, 305-8571, Japan. e-mail: kanekoha@math.tsukuba.ac.jp
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Abstract

Let b ⩾ 2 be an integer. Among other results we establish, in a quantitative form, that any sufficiently large integer which is not a multiple of b cannot simultaneously be divisible only by very small primes and have very few nonzero digits in its representation in base b.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 165 , Issue 3 , November 2018 , pp. 533 - 540
Copyright
Copyright © Cambridge Philosophical Society 2017 

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References

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