Mathematica Notebooks:

The following Mathematica notebooks are made available for use with the textbook Number Theory with Computer Applications. The code is intented solely for educational use.

Chapter 2: Divisibility and Primes:

GCD Examples This notebook contains implementation of different algorithms for computing GCD and some examples, including an experiment on the frequency of quotients in the Euclidean algorithm.
Sieve of Eratosthenes An implementation of the Sieve of Eratosthenes along with the application to a simple primality test.
Factoring by Trial Division Demonstrates the simplest factoring method.

Chapter 3: Congruences

Chinese Remainder Theorem A demonstration of the solution of simultaneous congruences using the Chinese Remainder Theorem.

Chapter 5: Cryptography

Basic Routines A collection of Mathematica functions to simplify the frequency analysis of characters and digrams and trigrams for section 5.1

Chapter 6: Primality Testing and Factoring

Pseudoprimes and Strong Pseudoprimes Examples of pseudoprime test and the strong pseudoprime test.
Pollard p-1 factoring method An implementation in Mathematica that demonstrates the algorithm step by step.

Chapter 11: Continued Fractions

Simple Continued Fractions Examples of construction of simple continued fractions and computation of their convergents.
Continued Fractions of Quadratic Irrationals Code to compute the continued fraction expansion of a real quadratic irrational number.