Article
Products of Integers With Few Nonzero Digits
Authors
and
Abstract
Let \( s(n) \) be the number of nonzero bits in the binary digital expansion
of the integer \( n \). We study, for fixed \( k,\ell,m \), the Diophantine system
\[
s(ab)=k,\qquad s(a)=\ell,\qquad s(b)=m,
\]
in odd integer variables \( a,b \). When \( k=2 \) or \( k=3 \), we establish a
bound on \( ab \) in terms of \( \ell \) 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 \( \ell \) and \( m \).
Keywords
sum of digits, digital expansion, factors.
Citation
Kaneko, H. & Stoll, T. (2022). Products of integers with few nonzero digits. Uniform Distribution Theory, 17(1), 71–89. https://doi.org/10.2478/UDT-2022-0006
H. Kaneko and T. Stoll, “Products of integers with few nonzero digits,” Uniform Distribution Theory, vol. 17, no. 1, pp. 71–89, 2022, doi: 10.2478/UDT-2022-0006.
Kaneko H, Stoll T. Products of integers with few nonzero digits. Uniform Distribution Theory. 2022;17(1):71–89. doi:10.2478/UDT-2022-0006.
Kaneko, H. and Stoll, T. (2022), ‘Products of integers with few nonzero digits’, Uniform Distribution Theory, 17(1), pp. 71–89. Available at: https://doi.org/10.2478/UDT-2022-0006.
Kaneko, Hajime, and Thomas Stoll. “Products of Integers with Few Nonzero Digits.” Uniform Distribution Theory, vol. 17, no. 1, 2022, pp. 71–89. https://doi.org/10.2478/UDT-2022-0006.
Kaneko, Hajime, and Thomas Stoll. “Products of Integers with Few Nonzero Digits.” Uniform Distribution Theory 17, no. 1 (2022): 71–89. https://doi.org/10.2478/UDT-2022-0006.
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Published by: Engineering Journals
