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Problems of Number Theory in Mathematical Competitions

Yu Hong-Bing
World Scientific
Publication Date: 
Number of Pages: 
Mathematical Olympiad Series 2
Problem Book
[Reviewed by
Tom Schulte
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This slim volume of 106 pages is dedicated to elementary number theory not as a field of mathematics per se, but as it may appear in mathematical competitions. However, in exhibiting basic concepts and methods in elementary number theory through detailed explanation and examples, the author created a work that can be an adjunct to any introduction to number theory, even without competitions being considered. Solutions for all problems are given and topics benefit from many, detailed examples.

Topics covered start at divisibility including gcd, lcm, and Bézout’s Identity. Also covered is primality and factorization, including the Chinese Remainder Theorem. Indeterminate systems get a special focus in two chapters. Fermat’s Little Theorem and the Euler function are touched on, and there is a chapter devoted to multiplicative order as well. There are two chapters that review over previous content by highlighting problems from Mathematical Olympiads.

The book’s specific goal is to teach tricks of problem-solving, but a byproduct of reading it is a wide introduction to topics of elementary number theory. Undergraduates struggling with this area, or any interested reader, will benefit from following through this book’s examples and exercises.

Tom Schulte teaches mathematics at Oakland Community College. He enjoys memoirs, history, and a good game of chess.

  • Divisibility
  • Greatest Common Divisors and Least Common Multiples
  • Prime Numbers and Unique Factorization Theorem
  • Indeterminate Equations (I)
  • Selected Lectures on Competition Problems (I)
  • Congruence
  • Some Famous Theorems in Number Theory
  • Order and Its Application
  • Indeterminate Equations (II)
  • Selected Lectures on Competition Problems (II)