This text teaches students about the role of number theory in pure mathematics and its important applications to cryptography and other areas. Designed for a one-semester undergraduate course in number theory, the book offers many pedagogical features. "Check your understanding" problems assess whether students have learned essential information. At the end of every chapter, exercises reinforce an understanding of the material. Other exercises introduce new and interesting ideas while computer exercises reflect the kinds of explorations that number theorists often carry out in their research.

Introduction. Divisibility. Linear Diophantine Equations. Unique Factorization. Applications of Unique Factorization. Congruences. Fermat, Euler, Wilson. Cryptographic Applications. Order and Primitive Roots. More Cryptographic Applications. Quadratic Reciprocity. Primality and Factorization. Sums of Squares. Arithmetic Functions. Continued Fractions. Recent Developments. Appendices. Index.

James S. Kraft teaches mathematics at the Gilman School. He has previously taught at the University of Rochester, St. Mary's College of California, and Ithaca College. He has also worked in communications security. Dr. Kraft has published several research papers in algebraic number theory. He received his Ph.D. from the University of Maryland.

Lawrence C. Washington is a professor of mathematics and Distinguished Scholar-Teacher at the University of Maryland. Dr. Washington has published extensively in number theory, including books on cryptography (with Wade Trappe), cyclotomic fields, and elliptic curves. He received his Ph.D. from Princeton University.