Stein W. Elementary Number Theory. Primes, Congruences, and Secrets...2017

Textbook in PDF format

This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergraduate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The reader is strongly encouraged to do every exercise in this book, checking their answers in the back (where many, but not all, solutions are given). Also, throughout the text there, are examples of calculations done using the powerful free open source mathematical software system Sage (http://www.sagemath.org), and the reader should try every such example and experiment with similar examples. The reader should know how to read and write mathematical proofs and must know the basics of groups, rings, and fields. Thus, the prerequisites for this book are more than the prerequisites for most elementary number theory books, while still being aimed at undergraduates.
Prime Numbers.
The Ring of Integers Modulo n.
Public-key Cryptography.
Quadratic Reciprocity.
Continued Fractions.
Elliptic Curves.
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