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Perfect powers with few binary digits and related Diophantine problems, II

  • MICHAEL A. BENNETT (a1), YANN BUGEAUD (a2) and MAURICE MIGNOTTE (a2)

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.

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Perfect powers with few binary digits and related Diophantine problems, II

  • MICHAEL A. BENNETT (a1), YANN BUGEAUD (a2) and MAURICE MIGNOTTE (a2)

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