Fundamental Number Theory with Applications, 2nd Edition

An update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. The substantial amount of reorganizing makes this edition clearer and more elementary in its coverage.

New to the Second Edition

• Removal of all advanced material to be even more accessible in scope
•  New fundamental material, including partition theory, generating functions, and combinatorial number theory
• Expanded coverage of random number generation, Diophantine analysis, and additive number theory
• More applications to cryptography, primality testing, and factoring
• An appendix on the recently discovered unconditional deterministic polynomial-time algorithm for primality testing

Taking a truly elementary approach to number theory, this text supplies the essential material for a first course on the subject. Placed in highlighted boxes to reduce distraction from the main text, nearly 70 biographies focus on major contributors to the field. The presentation of over 1,300 entries in the index maximizes cross-referencing so students can find data with ease.

Table of Contents

Chapter 1 Arithmetic Of The Integers
Chapter 2 Modular Arithmetic
Chapter 3 Primitive Roots
Chapter 4 Quadratic Residues
Chapter 5 Simple Continued Fractions And Diophantine Approximation
Chapter 6 Additivity — Sums Of Powers
Chapter 7 Diophantine Equations
Appendix A: Fundamental Facts
Appendix B: Complexity
Appendix C: Primes < 9547 and Least Primitive Roots
Appendix D: Indices
Appendix E: The ABC Conjecture
Appendix F: Primes is in P