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On the non-randomness of modular arithmetic progressions: a solution to a problem by V. I. Arnold

Abstract : 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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  • HAL Id : hal-01184715, version 1

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Eda Cesaratto, Alain Plagne, Brigitte Vallée. On the non-randomness of modular arithmetic progressions: a solution to a problem by V. I. Arnold. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. pp.271-288. ⟨hal-01184715⟩

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