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| Title Details: | |
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Congruences |
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| 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: | 08-10-2015 |
| 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 |