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On the non-randomness of modular arithmetic progressions: a solution to a problem by V. I. Arnold
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities (2006).

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We solve a problem by V. I. Arnold dealing with "how random" modular arithmetic progressions can be. After making precise how Arnold proposes to measure the randomness of a modular sequence, we show that this measure of randomness takes a simplified form in the case of arithmetic progressions. This simplified expression is then estimated using the methodology of dynamical analysis, which operates with tools coming from dynamical systems theory. In conclusion, this study shows that modular arithmetic progressions are far from behaving like purely random sequences, according to Arnold's definition. 
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     author = {Cesaratto, Eda and Plagne, Alain and Vall\'ee, Brigitte},
     title = {On the non-randomness of modular arithmetic progressions: a solution to a problem by {V.} {I.} {Arnold}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities},
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     doi = {10.46298/dmtcs.3510},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3510/}
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Cesaratto, Eda; Plagne, Alain; Vallée, Brigitte. On the non-randomness of modular arithmetic progressions: a solution to a problem by V. I. Arnold. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities (2006). doi : 10.46298/dmtcs.3510. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3510/

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