An introduction to number theory, with emphasis on a broad range of computational issues. Mathematica files (on CD-ROM) with all the commands and programs are included as a tool for motivation and explanation. This book covers the theoretical structure of number theory, but expands with the software into exploration of many topics including factoring algorithms, primality testing, the RSA public-key cryptosystem. Unusual and advanced topics are also covered including check digit schemes, continued fractions, Pell's equation, and the Gaussian primes.
Fundamentals | Congruences, Equations, and Powers | Euler's Function | Prime Numbers | Some Applications | Quadratic Residues | Continued Fractions | Prime Testing with Lucas Sequences | Prime Imaginaries and Imaginary Primes | Appendix A: Mathematica Basics | Appendix B: Lucas Certificates Exist | References