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© 2011

Problem-Solving and Selected Topics in Number Theory

In the Spirit of the Mathematical Olympiads

Textbook

Table of contents

  1. Front Matter
    Pages i-xv
  2. Michael Th. Rassias
    Pages 1-14
  3. Michael Th. Rassias
    Pages 15-28
  4. Michael Th. Rassias
    Pages 29-35
  5. Michael Th. Rassias
    Pages 37-49
  6. Michael Th. Rassias
    Pages 51-78
  7. Michael Th. Rassias
    Pages 79-82
  8. Michael Th. Rassias
    Pages 83-98
  9. Michael Th. Rassias
    Pages 99-101
  10. Michael Th. Rassias
    Pages 103-145
  11. Michael Th. Rassias
    Pages 147-162
  12. Michael Th. Rassias
    Pages 163-290
  13. Michael Th. Rassias
    Pages 291-316
  14. Back Matter
    Pages 317-324

About this book

Introduction

This book is designed to introduce some of the most important theorems and results from number theory while testing the reader’s understanding through carefully selected Olympiad-caliber problems. These problems and their solutions provide the reader with an opportunity to sharpen their skills and to apply the theory. This framework guides the reader to an easy comprehension of some of the jewels of number theory The book is self-contained and rigorously presented. Various aspects will be of interest to graduate and undergraduate students in number theory, advanced high school students and the teachers who train them for mathematics competitions, as well as to scholars who will enjoy learning more about number theory. Michael Th. Rassias has received several awards in mathematical problem solving competitions including two gold medals at the Pan-Hellenic Mathematical Competitions of 2002 and 2003 held in Athens, a silver medal at the Balkan Mathematical Olympiad of 2002 held in Targu Mures, Romania and a silver medal at the 44th International Mathematical Olympiad of 2003 held in Tokyo, Japan.

Keywords

Mathematics Competition Mathematics Olympiad Number Theory Problem-Solving

Authors and affiliations

  1. 1., Department of Pure Mathematics and MatheUniversity of CambridgeCambridgeUnited Kingdom

About the authors

Michael Th. Rassias has received several awards in mathematical problem solving competitions including two gold medals at the Pan-Hellenic Mathematical Competitions of 2002 and 2003 held in Athens, a silver medal at the Balkan Mathematical Olympiad of 2002 held in Targu Mures, Romania and a silver medal at the 44th International Mathematical Olympiad of 2003 held in Tokyo, Japan.

Bibliographic information

  • Book Title Problem-Solving and Selected Topics in Number Theory
  • Book Subtitle In the Spirit of the Mathematical Olympiads
  • Authors Michael Th. Rassias
  • DOI https://doi.org/10.1007/978-1-4419-0495-9
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-1-4419-0494-2
  • Softcover ISBN 978-1-4899-8194-3
  • eBook ISBN 978-1-4419-0495-9
  • Edition Number 1
  • Number of Pages XIV, 324
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Number Theory
  • Buy this book on publisher's site
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Reviews

From the reviews:

"Opening at random any page of this delightful book, the reader will almost certainly find something intriguing and interesting on the page. The book is an excellent "training manual'' to use in preparation for (the number theoretic portions of) mathematical competitions and olympiads. The dedicated problem-solver would do well to avoid too early reference to the "Solutions'' chapter. At the proper time, however, carefully studying this chapter is as rewarding as the earlier part of the book. This is a book that belongs in all academic libraries—from high school through graduate level." 

— F. J. Papp, Mathematical Reviews

“The book under review is not the only book which focuses on olympiad problems in number theory, but because of its structure (containing topics and problems), it is also useful for teaching. I highly recommend this book for students and teachers of MOs.”

—Mehdi Hassani, MAA Reviews

"[This book] appears like a confession of a young mathematician to students of his age, revealing to them some of his preferred topics in number theory based on solutions of particular problems... Michael does not limit himself to those particular problems. He also deals with topics in classical number theory and provided extensive proofs of the results...It offers pleasant reading for young people who are interested in mathematics. They will be guided to easy comprehension of some of the jewels of number theory."

—Preda Mihăilescu, EMS Newsletter March 2011

“The present book provides a wonderful presentation of concepts and ideas as well as problems with their solutions in Number Theory. Although most of the problems solved in this book were given in international mathematical contests and hence are of high level of complexity, the author has succeeded in providing solutions and extensive step-by-step proofs in a rigorous yet very simple and fascinating way. Even though the author is a very young mathematician (of only 23 years), he is an outstanding specialist in this field."

—Dorin Andrica, Zentralblatt MATH

“Containing all of the things he suggests one should know to compete successfully in an IMO competition. The book is based on his undergraduate thesis on computational number theory … . it is so much more than basic things one should know, providing a rich overview of the many beautiful ideas in number theory. … Plus, the text is enriched with historical comments, special problem-solving techniques, and a wealth of problems to investigate. … Summing Up: Recommended. Academic readership, all levels.”

—Johnson, Choice, Vol. 49 (4), December, 2011