Elementary Number Theory: Primes, Congruences, and Secrets A Computational Approach

Elementary Number Theory: Primes, Congruences, and Secrets A Computational Approach by William Stein is a textbook published by Springer on January 8, 2009, comprising 166 pages. This edition presents a thorough exploration of classical elementary number theory and elliptic curves, addressing foundational topics such as primes, factorization, continued fractions, and quadratic forms, particularly in relation to cryptography and computational methods.

Readers will find that the book is structured in two main parts. The first part covers elementary topics and their applications to significant open research problems, while the second part delves into elliptic curves and their relevance to algorithmic challenges and various number theory problems, including Fermat’s Last Theorem and the Congruent Number Problem. This text is designed for undergraduates who possess a basic understanding of abstract algebra, including concepts like rings, fields, and finite abelian groups.