1. bookVolumen 17 (2022): Edición 1 (December 2022)
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eISSN
2309-5377
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30 Dec 2013
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Products of Integers with Few Nonzero Digits

Publicado en línea: 31 May 2022
Volumen & Edición: Volumen 17 (2022) - Edición 1 (December 2022)
Páginas: 11 - 28
Recibido: 30 Jun 2021
Aceptado: 23 Nov 2021
Detalles de la revista
License
Formato
Revista
eISSN
2309-5377
Primera edición
30 Dec 2013
Calendario de la edición
2 veces al año
Idiomas
Inglés
Abstract

Let s(n) be the number of nonzero bits in the binary digital expansion of the integer n. We study, for fixed k, ℓ, m, the Diophantine system

s(ab)= k, s(a)= ℓ, and s(b)= m

in odd integer variables a, b.When k =2 or k = 3, we establish a bound on ab in terms of and m. While such a bound does not exist in the case of k =4, we give an upper bound for min{a, b} in terms of and m.

Keywords

MSC 2010

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