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Title Details:
Congruences
Authors: Antoniadis, Ioannis
Kontogeorgis, Aristeidis
Reviewer: Theochari Apostolidou, Theodora
Subject: MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > NUMBER THEORY
Keywords:
Prime Numbers
Diophantine Equations
Congruences
Quadratic Residues
Law Of Quadratic Reciprocity
Primitive Roots
Indexes
Primality Testing
Factorization
Continued Fractions
Pell Equation
Quadratic Forms
Quadratic Number Fields
Coding Theory
Integral Basis
Discriminant
Fundamental Unit
Decomposition Law
Class Number
Pseudoprimes
Carmichael Numbers
Jacobi Symbol
L-series
Legendre Symbol
Fibonacci And Lucas Numbers
Cryptography
Description:
Abstract:
Basic properties of congruences.
Fermat's little theorem, Eulers φ-function.
The theorem of Euler, theorem of Redei.

Systems of congruences.

Applications: divisibility criteria, Orthodox easter computation,
raising to power and square roots mod m.

Cryptography:
Non symmetric cryptography: the RSA system

Coding theory:
ISBN system

Higher congruences, Wilson theorem, factorization.
Pseudoprimes, Carmichael numbers, Miller-Rabin algorithm, Dixon's p-1 and rho Pollards
factorization algorithms.
Linguistic Editors: Kalliaras, Dimitris
Type: Chapter
Creation Date: 2015
Item Details:
License: http://creativecommons.org/licenses/by-nc-nd/3.0/gr
Handle http://hdl.handle.net/11419/111
Bibliographic Reference: Antoniadis, I., & Kontogeorgis, A. (2015). Congruences [Chapter]. In Antoniadis, I., & Kontogeorgis, A. 2015. Number Theory and Applications [Undergraduate textbook]. Kallipos, Open Academic Editions. https://hdl.handle.net/11419/111
Language: Greek
Is Part of: Number Theory and Applications
Publication Origin: Kallipos, Open Academic Editions