Article Dans Une Revue Uniform Distribution Theory Année : 2021

Products of integers with few nonzero digits

Résumé

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.

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Dates et versions

hal-03468234 , version 1 (10-07-2021)
hal-03468234 , version 2 (07-12-2021)

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Hajime Kaneko, Thomas Stoll. Products of integers with few nonzero digits. Uniform Distribution Theory, In press, ⟨10.48550/arXiv.2112.03077⟩. ⟨hal-03468234v2⟩
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