Number Theory: Structures, Examples, and Problems (2009)

One of the liveliest branches of mathematics, number theory is noted for its theoretical depth and applications to other fields. Number theory is replete with sophisticated problems. However, at its foundation are basic, elementary ideas that can stimulate and challenge beginning students. This introductory textbook takes a problem-solving approach to number theory, situating each concept within the framework of an example or a problem for readers to solve. Starting with the essentials, the text includes coverage of divisibility, unique factorization, modular arithmetic and the Chinese Remainder Theorem, Diophantine equations, and binomial coefficients. By emphasizing examples and applications the authors motivate and engage readers. The exposition proceeds incrementally from first principles, starting with the natural numbers and then intuitively and rigorously uncovering deeper properties. A comprehensive index and selected solutions complete the work.