Geodesic
Linear Congruences in Continued Fractions on Finite Alphabets
Matematičeskie zametki, Tome 103 (2018) no. 6, pp. 853-862 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {I. D. Kan},
     title = {Linear {Congruences} in {Continued} {Fractions} on {Finite} {Alphabets}},
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I. D. Kan. Linear Congruences in Continued Fractions on Finite Alphabets. Matematičeskie zametki, Tome 103 (2018) no. 6, pp. 853-862. http://geodesic.mathdoc.fr/item/MZM_2018_103_6_a4/

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