Author:
BENNETT MICHAEL A.,BUGEAUD YANN,MIGNOTTE MAURICE
Abstract
AbstractWe prove that if q ≥ 5 is an integer, then every qth power of an integer contains at least 5 nonzero digits in its binary expansion. This is a particular instance of one of a collection of rather more general results, whose proofs follow from a combination of refined lower bounds for linear forms in Archimedean and non-Archimedean logarithms with various local arguments.
Publisher
Cambridge University Press (CUP)
Cited by
13 articles.
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1. On the binary digits of n and n2;Theoretical Computer Science;2023-01
2. Products of Integers with Few Nonzero Digits;Uniform distribution theory;2022-05-31
3. On sparse perfect powers;Moscow Journal of Combinatorics and Number Theory;2021-12-31
4. Linear Forms in Logarithms and Applications;IRMA LECT MATH THEOR;2018-02-28
5. On the digital representation of smooth numbers;Mathematical Proceedings of the Cambridge Philosophical Society;2017-08-29