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Matematicheskie Zametki, 2022, Volume 111, Issue 1, Pages 117–124
DOI: https://doi.org/10.4213/mzm13075 (Mi mzm13075) 		 
Quotients of Dense Subsets of Integers and Short Distances between Product Elements

Yu. N. Shteinikov

Scientific Research Institute for System Analysis of the Russian Academy of Sciences, Moscow
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DOI: https://doi.org/10.4213/mzm13075
Abstract: The lower bound on the set of quotients of two subsets $A$, $B$ from finite intervals of natural numbers with positive density is refined. This bound yields an estimate of short distances between the elements of the product of these two sets. In this paper, we borrow problems, approaches, and arguments proposed in [5] of J. Cilleruelo, D. S. Ramana, and O. Ramaré.
Keywords: divisibility, products, quotients, distances.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 0580-2021-0011
This work was carried out within the framework of the state assignment for conducting fundamental scientific research (grant 0580-2021-0011).
Received: 19.03.2021
Revised: 20.07.2021
English version:
Mathematical Notes, 2022, Volume 111, Issue 1, Pages 132–138
DOI: https://doi.org/10.1134/S000143462201014X
Bibliographic databases:
Document Type: Article
UDC: 511.321
Language: Russian
Citation: Yu. N. Shteinikov, “Quotients of Dense Subsets of Integers and Short Distances between Product Elements”, Mat. Zametki, 111:1 (2022), 117–124; Math. Notes, 111:1 (2022), 132–138
Citation in format AMSBIB
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