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Elementary number theory / by James S. Kraft and Lawrence C. Washington.

By: Kraft, James S [author.].
Contributor(s): Washington, Lawrence C [author.] | Taylor and Francis.
Material type: materialTypeLabelBookPublisher: Boca Raton, FL : Chapman and Hall/CRC, an imprint of Taylor and Francis, 2014Edition: First edition.Description: 1 online resource (411 pages) : 9 illustrations.Content type: text Media type: computer Carrier type: online resourceISBN: 9780429171970.Subject(s): Number theory | MATHEMATICS / Algebra / Intermediate | MATHEMATICS / Combinatorics | MATHEMATICS / Number TheoryAdditional physical formats: Print version: : No titleDDC classification: 512.7/2 Online resources: Click here to view.
Contents:
chapter Introduction -- chapter 1 - Divisibility -- chapter 2 - Linear Diophantine Equations -- chapter 3 - Unique Factorization -- chapter 4 - Applications of Unique Factorization -- chapter 5 - Congruences -- chapter 6 - Fermat, Euler, Wilson -- chapter 7 - Cryptographic Applications -- chapter 8 - Order and Primitive Roots -- chapter 9 - More Cryptographic Applications -- chapter 10 - Quadratic Reciprocity -- chapter 11 - Primality and Factorization -- chapter 12 - Sums of Squares -- chapter 13 - Arithmetic Functions -- chapter 14 - Continued Fractions -- chapter 15 - Recent Developments.
Abstract: Elementary Number Theory takes an accessible approach to teaching students about the role of number theory in pure mathematics and its important applications to cryptography and other areas. The first chapter of the book explains how to do proofs and includes a brief discussion of lemmas, propositions, theorems, and corollaries. The core of the text covers linear Diophantine equations; unique factorization; congruences; Fermat's, Euler's, and Wilson's theorems; order and primitive roots; and quadratic reciprocity. The authors also discuss numerous cryptographic topics, such as RSA and discrete logarithms, along with recent developments.
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chapter Introduction -- chapter 1 - Divisibility -- chapter 2 - Linear Diophantine Equations -- chapter 3 - Unique Factorization -- chapter 4 - Applications of Unique Factorization -- chapter 5 - Congruences -- chapter 6 - Fermat, Euler, Wilson -- chapter 7 - Cryptographic Applications -- chapter 8 - Order and Primitive Roots -- chapter 9 - More Cryptographic Applications -- chapter 10 - Quadratic Reciprocity -- chapter 11 - Primality and Factorization -- chapter 12 - Sums of Squares -- chapter 13 - Arithmetic Functions -- chapter 14 - Continued Fractions -- chapter 15 - Recent Developments.

Elementary Number Theory takes an accessible approach to teaching students about the role of number theory in pure mathematics and its important applications to cryptography and other areas. The first chapter of the book explains how to do proofs and includes a brief discussion of lemmas, propositions, theorems, and corollaries. The core of the text covers linear Diophantine equations; unique factorization; congruences; Fermat's, Euler's, and Wilson's theorems; order and primitive roots; and quadratic reciprocity. The authors also discuss numerous cryptographic topics, such as RSA and discrete logarithms, along with recent developments.

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