Geodesic
Quotients of Dense Subsets of Integers
Matematičeskie zametki, Tome 111 (2022) no. 1, pp. 117-124

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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
Mots-clés : quotients, distances. 
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     author = {Yu. N. Shteinikov},
     title = {Quotients of {Dense} {Subsets} of {Integers}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {117--124},
     publisher = {mathdoc},
     volume = {111},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_111_1_a10/}
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Yu. N. Shteinikov. Quotients of Dense Subsets of Integers. Matematičeskie zametki, Tome 111 (2022) no. 1, pp. 117-124. http://geodesic.mathdoc.fr/item/MZM_2022_111_1_a10/