1. bookVolumen 17 (2022): Heft 1 (December 2022)
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License
Format
Zeitschrift
eISSN
2309-5377
Erstveröffentlichung
30 Dec 2013
Erscheinungsweise
2 Hefte pro Jahr
Sprachen
Englisch
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Products of Integers with Few Nonzero Digits

Online veröffentlicht: 31 May 2022
Volumen & Heft: Volumen 17 (2022) - Heft 1 (December 2022)
Seitenbereich: 11 - 28
Eingereicht: 30 Jun 2021
Akzeptiert: 23 Nov 2021
Zeitschriftendaten
License
Format
Zeitschrift
eISSN
2309-5377
Erstveröffentlichung
30 Dec 2013
Erscheinungsweise
2 Hefte pro Jahr
Sprachen
Englisch
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.

MSC 2010

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