
Preface  Introduction  Preview Material  Table of Contents  Index  Supplementary Material 
Student Mathematical Library 2014; 244 pp; softcover Volume: 70 ISBN10: 0821898833 ISBN13: 9780821898833 List Price: US$45 Institutional Members: US$36 All Individuals: US$36 Order Code: STML/70 See also: Analytic Number Theory: Exploring the Anatomy of Integers  JeanMarie De Koninck and Florian Luca Not Always Buried Deep: A Second Course in Elementary Number Theory  Paul Pollack The Prime Numbers and Their Distribution  Gerald Tenenbaum and Michel Mendes France  How can you tell whether a number is prime? What if the number has hundreds or thousands of digits? This question may seem abstract or irrelevant, but in fact, primality tests are performed every time we make a secure online transaction. In 2002, Agrawal, Kayal, and Saxena answered a longstanding open question in this context by presenting a deterministic test (the AKS algorithm) with polynomial running time that checks whether a number is prime or not. What is more, their methods are essentially elementary, providing us with a unique opportunity to give a complete explanation of a current mathematical breakthrough to a wide audience. RempeGillen and Waldecker introduce the aspects of number theory, algorithm theory, and cryptography that are relevant for the AKS algorithm and explain in detail why and how this test works. This book is specifically designed to make the reader familiar with the background that is necessary to appreciate the AKS algorithm and begins at a level that is suitable for secondary school students, teachers, and interested amateurs. Throughout the book, the reader becomes involved in the topic by means of numerous exercises. Readership Undergraduate students interested in number theory, cryptography, and computer science. 


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