Fundamental number theory with applications

Author(s)

• Mollin, Richard A.

Bibliographic Information

Fundamental number theory with applications

Richard A. Mollin

（Discrete mathematics and its applications / Kenneth H. Rosen, series editor）

CRC Press, c1998

• alk. paper

Other Title

The CRC Press series on discrete mathematics and its applications

Note

Includes bibliographical references (p. 423-425) and index

Description and Table of Contents

Description

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.

Table of Contents

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

by "Nielsen BookData"

Details

• NCID: BA36166858
• ISBN:
  • 0849339871
• LCCN: 97033279
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Boca Raton
• Pages/Volumes: xii, 439 p.
• Size: 24 cm
• Classification:
  • LCC : QA241
  • DC21 : 512/.72
• Subject Headings:
  • LCSH : Number theory
• Parent Bibliography ID:
  • BA25247299