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This article is cited in 4 scientific papers (total in 4 papers)
Linear Congruences in Continued Fractions on Finite Alphabets
I. D. Kan Moscow Aviation Institute (National Research University)
Abstract:
A linear homogeneous congruence $ay\equiv bY \,(\operatorname{mod}{q})$ is considered and an order-sharp upper bound for the number of its solutions is proved. Here $a$, $b$, and $q$ are given jointly coprime numbers and $y$ and $Y$ are coprime variables in a given closed interval such that the number $y/Y$ can be expanded in a continued fraction with partial quotients from some alphabet $\mathbf{A}\subseteq\mathbb{N}$. For $\mathbf{A}=\mathbb{N}$ (and without the assumption that $y$ and $Y$ are coprime), a similar problem was solved by N. M. Korobov.
Keywords:
linear congruence, continued fraction.
Received: 18.05.2017 Revised: 14.07.2017
Citation:
I. D. Kan, “Linear Congruences in Continued Fractions on Finite Alphabets”, Mat. Zametki, 103:6 (2018), 853–862; Math. Notes, 103:6 (2018), 911–918
Linking options:
https://www.mathnet.ru/eng/mzm12006https://doi.org/10.4213/mzm12006 https://www.mathnet.ru/eng/mzm/v103/i6/p853
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Abstract page: | 329 | Full-text PDF : | 100 | References: | 28 | First page: | 22 |
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