Elementary Number Theory and Its Applications

Author: (USA) Rosen (Rosen/K.H.)
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 topic. 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 an extensive and diverse set of exercises. Many routine exercises are included to train basic skills, with both odd-numbered and even-numbered exercises provided in this category. A large number of medium-difficulty exercises help students combine concepts to form new results. Many other exercises or exercise sets are designed to develop new concepts. Challenging exercises are also sufficient, marked with a single asterisk for difficult problems and a double asterisk for very difficult ones. Some exercises include results that will be used in later chapters of the text, marked with a finger symbol. Such exercises should be assigned by instructors when appropriate. This book includes new discoveries in number theory, describing the status of many unsolved problems, such as new theoretical achievements. The new discoveries about prime numbers and factorization in September 2004 are included in this edition's second printing. These findings will help readers understand that number theory is an extremely active research field, and they may even have the opportunity to participate in the discovery of new primes.