Number Theory: Structures, Examples, and Problems

This introductory textbook takes a problem-solving approach to number theory, situating each concept within the framework of an example or a problem for solving. Starting with the essentials, the text covers divisibility, unique factorization, modular arithmetic and the Chinese Remainder Theorem, Diophantine equations, binomial coefficients, Fermat and Mersenne primes and other special numbers, and special sequences. Included are sections on mathematical induction and the pigeonhole principle, as well as a discussion of other number systems. By emphasizing examples and applications the authors motivate and engage readers.

• 104 Number Theory Problems: From the Training of the USA IMO Team
• 102 Combinatorial Problems
• Problem-Solving Strategies (Problem Books in Mathematics)
• A Path to Combinatorics for Undergraduates: Counting Strategies
• 103 Trigonometry Problems: From the Training of the USA IMO Team
• 105 Algebra Problems from the AwesomeMath Summer Program
• Euclidean Geometry in Mathematical Olympiads (Maa Problem)
• Number Theory (Dover Books on Mathematics)
• How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library)
• Challenging Problems in Geometry (Dover Books on Mathematics)