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Journal

Uniform Distribution Theory (UDT)


Volume & Issue

UDT. Volume 17. Issue 1


Published on

June, 2022


Pages

11-28


DOI

https://doi.org/10.2478/udt-2022-0006

Article

Products of Integers with Few Nonzero Digits


Authors

Hajime Kaneko and Thomas Stoll


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 ℓ 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 ℓ and m.


Citation

Kaneko, H. & Stoll, T. (2022). Products of Integers with Few Nonzero Digits. Uniform distribution theory, 17(1), 11-28. https://doi.org/10.2478/udt-2022-0006