Number Theory

This book covers an elementary introduction to Number Theory, with an emphasis on presenting and proving a large number of theorems. No attempts will be made to derive number theory from set theory and no knowledge of Calculus will be assumed. It is important to convince yourself of the truth of each proof as you work through the book, and make sure you have a complete understanding. For those who wish to use this as a reference book, an index of theorems will be given.

• Notation and Introduction to Proof
• Axioms
• Elementary Divisibility
• Pythagorean Triples
• Unique Factorization
• Congruences
• Diophantine Equations
• Irrational Rational and Transcendental Numbers
• Rings and Ideals
• Gaussian Integers
• Continued Fractions
• Quadratic Fields
• Index of Theorems with Proofs
• Additional Theorems with proof sketches
• Exercises in Proof

• 32-Bit Linear Congruential Generator

• Bibliography

• Proofs in Number Theory

• /Powers modulo 11
• /Powers modulo 19

• A Computational Introduction to Number Theory and Algebra (Shoup)-retrieved Dec 21, 2009