Mathematical Proceedings of the Cambridge Philosophical Society Perfect Powers with Few Binary Digits and Related Diophantine Problems, Ii Perfect Powers with Few Binary Digits and Related Diophantine Problems, Ii
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چکیده
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.
منابع مشابه
Perfect Powers with Few Binary Digits and Related Diophantine Problems, Ii
We prove that if q > 5 is an integer, then every q-th 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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