Number Theory

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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.

Chapters

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

Bibliography

See also

Externals links