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.

Approaches number theory from a problem-solving standpoint, presenting each concept in the framework of an example or problem The text progresses incrementally from simpler to more complex principles Covers modular arithmetic and the Chinese Remainder Theorem, Diophantine equations, binomial coefficients, Fermat and Mersenne primes and other special numbers, special sequences, and problems of density Includes sections on mathematical induction and the pigeonhole principle, and discusses other number systems Unconventional, essay-type, non-routine examples, exercises and problems, presented in an original fasion Includes supplementary material: sn.pub/extras

Autorentext

Teodora-Liliana Radulescu received her PhD in 2005 from Babes-Bolyai University of Cluj-Napoca, Romania, with a thesis on nonlinear analysis, and she is currently a professor of mathematics at the "Fratii Buzesti" National College in Craiova, Romania. She is a member of the American Mathematical Society and the Romanian Mathematical Society. She is also a reviewer for Mathematical Reviews and Zentralblatt fur Mathematik. Vicentiu Radulescu received both his PhD and the Habilitation at the Université Pierre et Marie Curie (Paris 6), and he is currently a professor of mathematics at the University of Craiova, Romania and a senior researcher at the Institute of Mathematics "Simion Stoilow" of the Romanian Academy in Bucharest, Romania. He has authored 9 books and over 100 articles. Titu Andreescu is an associate professor of mathematics at the University of Texas at Dallas. He is also firmly involved in mathematics contests and Olympiads, being the Director ofAMC (as appointed by the Mathematical Association of America), Director of MOP, Head Coach of the USA IMO Team and Chairman of the USAMO. He has also authored a large number of books on the topic of problem solving and Olympiad-style mathematics.

Inhalt
Fundamentals.- Divisibility.- Powers of Integers.- Floor Function and Fractional Part.- Digits of Numbers.- Basic Principles in Number Theory.- Arithmetic Functions.- More on Divisibility.- Diophantine Equations.- Some Special Problems in Number Theory.- Problems Involving Binomial Coefficients.- Miscellaneous Problems.- Solutions to Additional Problems.- Divisibility.- Powers of Integers.- Floor Function and Fractional Part.- Digits of Numbers.- Basic Principles in Number Theory.- Arithmetic Functions.- More on Divisibility.- Diophantine Equations.- Some Special Problems in Number Theory.- Problems Involving Binomial Coefficients.- Miscellaneous Problems.