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Title Details:
Congruences
Authors: Poulakis, Dimitrios
Reviewer: Tzanakis, Nikolaos
Subject: MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > NUMBER THEORY
MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > NUMBER THEORY > COMPUTATIONAL NUMBER THEORY
MATHEMATICS AND COMPUTER SCIENCE > COMPUTER SCIENCE
MATHEMATICS AND COMPUTER SCIENCE > COMPUTER SCIENCE > ALGORITHMS AND COMPLEXITY
Keywords:
Computational Number Theory
Congruences
Linear Congruences
Quadratic Residues
Finite Fields
Description:
Abstract:
Chapter 4 is devoted to the congruence relations of integers, the description of the properties of their classes and the running time of the execution of theirs basic operations. We study the resolution of linear congruences and theirs systems and we determine for which positive integers there are primitive roots modulo n. Furthermore, we introduce Legendre and Jacobi symbols and we present algorithms for the computation of Jacobi symbols and the solution of quadratic congruences. Finally, we introduce the notion of congruence between polynomials and we give the constuction of finite fields and some basic properties.
Table of Contents:
Chapter 4 contains the following sections:
5.1 Congruence Relations
5.2 Congruence Classes
5.3 Linear Congruences
5.4 The function φ of Euler
5.5 Order of an integer modulo n
5.6 Residus of m-th power
5.6.1 Legendre' s symbol
5.6.2 Jacobi' s symbol
5.6.3 Solving Quadratic Congruences
5.7 Finite Fields
5.7.1 Polynomial Congruences
5.7.2 Stucture of Finite Fields
5.8 Exercices
Bibliography
Technical Editors: Karakostas, Anastasios
Type: Chapter
Creation Date: 2015
Item Details:
License: http://creativecommons.org/licenses/by-nc-nd/3.0/gr
Handle http://hdl.handle.net/11419/1048
Bibliographic Reference: Poulakis, D. (2015). Congruences [Chapter]. In Poulakis, D. 2015. Computational Number Theory [Undergraduate textbook]. Kallipos, Open Academic Editions. https://hdl.handle.net/11419/1048
Language: Greek
Is Part of: Computational Number Theory
Number of pages 59
Publication Origin: Kallipos, Open Academic Editions