Elementary Number Theory and Its Applications (Fifth Edition)

Author: Kenneth
Publisher:
Publication Date: 2005-03-01
Features: The core of this book is to explain classical elementary number theory in a way that is both helpful and engaging. The historical context and significance of key results are documented. After presenting the fundamental material for each topic, the book discusses more complex results of the same theory. The main strength of this book lies in its inclusion of various applications of number theory. Once the necessary theory is established, applications are incorporated into the text in a flexible manner. These applications are designed to promote the extension of theory and illustrate the diverse uses of elementary number theory. Number theory is widely applied in cryptography, including classical cryptography, block ciphers, stream ciphers, public-key cryptographic systems, and cryptographic protocols. Other applications in computer science include fast integer multiplication, pseudorandom numbers, and checksums. Applications in many other fields, such as scheduling, telecommunication, entomology, and zoology, can also be found in the textbook. This textbook includes a vast and diverse set of exercises. Many routine exercises are included to train basic skills, with both odd-numbered and even-numbered problems included in this category. A large number of medium-difficulty problems help students combine concepts to form new results. Many other exercises or sets of exercises are designed to develop new concepts. Challenging problems are also sufficient, marked with a single asterisk for difficult problems and a double asterisk for very difficult ones. Some problems include results that will be used later in the text and are marked with a finger symbol. Such exercises should be assigned by instructors at appropriate times. This book includes new discoveries in number theory, describing the current status of many unsolved problems, such as new theoretical achievements. The new discoveries about prime numbers and factorization announced in September 2004 are included in this edition's second printing. These findings will help readers understand number theory as an extremely active research field, and they may even see or participate in the discovery of new primes.