Geodesic
On $q$-ary periodic sequences
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 1, Tome 179 (2020), pp. 34-36.

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We consider the problem of estimating the possible number of periods and the length of the periodic part of an irrational number depending on its measure of irrationality $\beta$. We state that the expansion of the fractional part of an irrational number $\alpha$ cannot start from the nonperiodic part of length $(1-\delta)N$ and end with the periodic part of the length $\delta N$, regardless of the numeral system.
Keywords: measure of irrationality
Mots-clés : $q$-ary decomposition. 
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A. H. Munos Vaskes. On $q$-ary periodic sequences. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 1, Tome 179 (2020), pp. 34-36. http://geodesic.mathdoc.fr/item/INTO_2020_179_a4/

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