ANALYSIS OF THE STRUCTURES OF ALGEBRAIC DYNAMICAL SYSTEMS BASED ON A COMPUTER SOLUTION OF THE GENERALIZED ARTIN HYPOTHESIS

DOI: https://doi.org/10.15276/eltecs.30.106.2019.14
Keywords: Generalized Artin's hypothesis. Algebraic dynamical system. Computer solution of the generalized Artin's hypothesis. Classification of prime numbers on the basis of a .

Abstract

The article considers the generalized Artin's hypothesis. The analysis of algebraic dynamical systems on the set of prime numbers is given. The properties of dynamic algebraic systems are studied.
Based on computer modeling, a solution of Artin’s generalized hypothesis was constructed. A classification of prime numbers for any natural number a 1 is constructed. The properties of classes of prime numbers are investigated. A method of structural analysis of algebraic dynamical systems with close values of generalized Artin constants was developed. It is established that for any a 1 each class has a probability measure, and the sum of the measures of the classes tends to unity.

Author Biographies

George Vostrov, Odessa National Polytechnic University
Candidate of Technical Sciences, Associate Professor
Roman Opiata, Odessa National Polytechnic University

PhD student

Published
2019-04-19
Issue
No. 30(106) (2019): Electrotechnic and Computer Systems
Section
Computer Systems, Networks and their Components

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