Computational Number Theory

A Course in Computational Number Theory uses the computer as a tool for motivation and explanation. The book is designed for the reader to quickly access a computer and begin doing personal experiments with the patterns of the integers. It presents and explains many of the fastest algorithms for working with integers. Traditional topics are covered, but the text also explores factoring algorithms, primality testing, the RSA public-key cryptosystem, and unusual applications such as check digit schemes and a computation of the energy that holds a salt crystal together. Advanced topics include continued fractions, Pells equation, and the Gaussian primes. The CD-ROM contains a Mathematicas package that has hundreds of functions that show step-by-step operation of famous algorithms. (The user must have Mathematica in order to use this package.) Also included is an auxiliary package that contains a database of all 53,000 integers below 10^16 that are 2- and 3-strong pseudoprimes. Users will also have access to an online guide that gives illustrative examples of each function.