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- Title
Perfect powers with few binary digits and related Diophantine problems, II.
- Authors
BENNETT, MICHAEL A.; BUGEAUD, YANN; MIGNOTTE, MAURICE
- Abstract
We 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.
- Subjects
BINARY number system; DIOPHANTINE analysis; PROBLEM solving; MATHEMATICAL combinations; MATHEMATICAL analysis; MATHEMATICAL proofs
- Publication
Mathematical Proceedings of the Cambridge Philosophical Society, 2012, Vol 153, Issue 3, p525
- ISSN
0305-0041
- Publication type
Article
- DOI
10.1017/S0305004112000345