Geodesic
Representations of positive integers in DBNS
Čebyševskij sbornik, Tome 14 (2013) no. 1, pp. 86-93 Cet article a éte moissonné depuis la source Math-Net.Ru

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With V. Ch. Salihov’s estimates of linear forms in $\ln2$ and $\ln3$ we improve the asymptotic estimate of number of terms in DBNS. 
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V. G. Chirskii; R. F. Shakirov. Representations of positive integers in DBNS. Čebyševskij sbornik, Tome 14 (2013) no. 1, pp. 86-93. http://geodesic.mathdoc.fr/item/CHEB_2013_14_1_a8/

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[2] Tijdeman R., “On the maximal distance between integers composed of small primes”, Composito mathematica, 28:2 (1974), 129–162 | MR

[3] Salikhov V. Kh., “O mere irratsionalnosti $\log 3$”, Doklady Akademii Nauk, 417:6 (2007), 753–755 | Zbl