Fundamental Number Theory with Applications (Discrete Mathematics and Its Applications)

Richard A. Mollin

ISBN 10: 0849339871 / ISBN 13: 9780849339875

Editore: CRC-Press, 1998

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Dati bibliografici

• Titolo: Fundamental Number Theory with Applications (Discrete Mathematics and Its Applications)
• Editore: CRC-Press
• Data di pubblicazione: 1998
• Lingua: Inglese
• ISBN 10: 0849339871
• ISBN 13: 9780849339875
• Rilegatura: hardcover
• Condizione: Good

Descrizione articolo

Riassunto

Beginning with the arithmetic of the rational integers and proceeding to an introduction of algebraic number theory via quadratic orders, Fundamental Number Theory with Applications reveals intriguing new applications of number theory. This text details aspects of computer science related to

cryptography

factoring

primality testing

complexity analysis

computer arithmetic

computational number theory
Fundamental Number Theory with Applications also covers:

Carmichael numbers

Dirichlet products

Jacobsthal sums

Mersenne primes

perfect numbers

powerful numbers

self-contained numbers
Numerous exercises are included, testing the reader's knowledge of the concepts covered, introducing new and interesting topics, and providing a venue to learn background material.
Written by a professor and author who is an accomplished scholar in this field, this book provides the material essential for an introduction to the fundamentals of number theory.

Contenuti

Arithmetic of the Integers
Introduction - Where We Begin and Why
The Fundamental Laws
Divisibility
Prime Numbers
Computer Arithmetic and Complexity
Applications to a Set of Quadratics
Congruences
The Basics
Linear Congruences
Arithmetic Functions - Euler's Totient
The Chinese Remainder Theorem
Polynomial Congruences and Thue's Theorem
Cryptography and Factoring
Quadratic Polynomials
Primitive Roots
Order
Existence
Indices
Primality Testing and Cryptography
Quadratic Orders, Ideals and Units
Quadratic Residues
The Quadratic Reciprocity Law
The Jacobi and Kronecker Symbols
Quadratic Polynomials and Primes
Quadratic Residues and Primality Testing
Applications to Quadratic Orders
Continued Fractions
Finite Continued Fractions
Infinite Continued Fractions
Periodic Continued Fractions
Continued Fractions and Factoring
The Continued Fraction Algorithm
Diophantine Equations
Sums of Squares
The Equation x2 - Dy2 = n
Diophantine Equations of Higher Degree
Elliptic Curves, Factoring, and Primality
Applications: Algebraic Number Theory
Appendices
A. Set Theory
B. Primes = 9547 and Least Primitive Roots
C. Tables of Special Primes
D. Cunningham Factorizations
E. Pseudoprimes and Carmichael Numbers
F. Indices
G. Values of Some Arithmetic Functions
H. The ABC Conjecture
I. The Prime Number Theorem
Solutions to Odd-Numbered Exercises
Bibliography
List of Symbols
Index