# An Introduction to Diophantine Equations: A Problem-Based Approach

## Titu Andreescu; Dorin Andrica; Ion Cucurezeanu

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This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions. An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants ― including Olympiad and Putnam competitors ― as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques.

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From the Back Cover:

This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The material is organized in two parts: Part I introduces the reader to elementary methods necessary in solving Diophantine equations, such as the decomposition method, inequalities, the parametric method, modular arithmetic, mathematical induction, Fermat's method of infinite descent, and the method of quadratic fields; Part II contains complete solutions to all exercises in Part I. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions.

An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants ― including Olympiad and Putnam competitors ― as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques.

Review:

From the reviews:

“This book is devoted to problems from mathematical competitions involving diophantine equations. ... Each chapter contains a large number of solved examples and presents the reader with problems whose solutions can be found in the book’s second part. This volume will be particularly interesting for participants in mathematical contests and their coaches. It will also give a lot of pleasure to everyone who likes to tackle elementary, yet nontrivial problems concerning diophantine equations.” (Ch. Baxa, Monatshefte für Mathematik, Vol. 167 (3-4), September, 2012)

“This book explains methods for solving problems with Diophantine equations that often appear in mathematical competitions at various levels. ... The book can be recommended to mathematical contest participants, but also to undergraduate students, advanced high school students and teachers.” (Andrej Dujella, Mathematical Reviews, Issue 2011 j)

“Diophantus’ Arithmetica is a collection of problems each followed by a solution...The book at hand is intended for high school students, undergraduates and math teachers. It is written in a language that everyone in these groups will be familiar with. The exposition is very lucid and the proofs are clear and instructive. The book will be an invaluable source for math contest participants and other math fans. It will be an excellent addition to any math library.” (Alex Bogomolny, The Mathematical Association of America, October, 2010)

“Diophantine analysis, the business of solving equations with integers, constitutes a subdiscipline within the larger field of number theory. One problem in this subject, Fermat's last theorem, till solved, topped most lists of the world's most celebrated unsolved mathematics problems, so the subject attracted much attention from mathematicians and even the larger public. Nevertheless, sophisticated 20th-century tools invented to attack Diophantine equations (algebraic number fields, automorphic forms, L-functions, adelic groups, etc.) have emerged as proper objects of study in their own right. So for a popular subject, modern lower-level works focused on the individual Diophantine equation (and not on big machines aimed generally at classes of such equations) are relatively rare. The present volume...fills this need...Summing Up: Recommended. Lower- and upper-division undergraduates and general readers.” (D.V. Feldman, Choice, July, 2010)

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## 1.An Introduction to Diophantine Equations: A Problem-Based Approach (Hardback)

Editore: BIRKHAUSER BOSTON INC, United States (2010)
ISBN 10: 0817645489 ISBN 13: 9780817645489
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Descrizione libro BIRKHAUSER BOSTON INC, United States, 2010. Hardback. Condizione libro: New. 2010 ed.. Language: English . Brand New Book. This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions. An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants - including Olympiad and Putnam competitors - as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques. Codice libro della libreria LIB9780817645489

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## 2.An Introduction to Diophantine Equations: A Problem-Based Approach (Hardback)

Editore: BIRKHAUSER BOSTON INC, United States (2010)
ISBN 10: 0817645489 ISBN 13: 9780817645489
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Descrizione libro BIRKHAUSER BOSTON INC, United States, 2010. Hardback. Condizione libro: New. 2010 ed.. Language: English . Brand New Book. This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions. An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants - including Olympiad and Putnam competitors - as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques. Codice libro della libreria LIB9780817645489

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## 3.An Introduction to Diophantine Equations

Editore: Birkhauser Boston Inc (2010)
ISBN 10: 0817645489 ISBN 13: 9780817645489
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Descrizione libro Birkhauser Boston Inc, 2010. HRD. Condizione libro: New. New Book.Shipped from US within 10 to 14 business days.THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria IP-9780817645489

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## 4.An Introduction to Diophantine Equations

Editore: Birkhäuser Boston 2010-09-13, New York |London (2010)
ISBN 10: 0817645489 ISBN 13: 9780817645489
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Descrizione libro Birkhäuser Boston 2010-09-13, New York |London, 2010. hardback. Condizione libro: New. Codice libro della libreria 9780817645489

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## 5.An Introduction to Diophantine Equations : A Problem-Based Approach

Editore: BirkhÃ¤user (2016)
ISBN 10: 0817645489 ISBN 13: 9780817645489
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Descrizione libro BirkhÃ¤user, 2016. Paperback. Condizione libro: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Codice libro della libreria ria9780817645489_lsuk

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## 6.An Introduction to Diophantine Equations. A Problem-Based Approach

Editore: BirkhÇÏuser (2010)
ISBN 10: 0817645489 ISBN 13: 9780817645489
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Descrizione libro BirkhÇÏuser, 2010. Hardback. Condizione libro: NEW. 9780817645489 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0285907

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## 7.An Introduction to Diophantine Equations

Editore: Birkhauser Boston Inc (2010)
ISBN 10: 0817645489 ISBN 13: 9780817645489
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Descrizione libro Birkhauser Boston Inc, 2010. HRD. Condizione libro: New. New Book. Delivered from our US warehouse in 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND.Established seller since 2000. Codice libro della libreria IP-9780817645489

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## 8.An Introduction to Diophantine Equations: A Problem-Based Approach

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ISBN 10: 0817645489 ISBN 13: 9780817645489
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Descrizione libro Birkhäuser, 2010. Condizione libro: New. Codice libro della libreria L9780817645489

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## 9.An Introduction to Diophantine Equations: A Problem-Based Approach

Editore: Birkhäuser (2017)
ISBN 10: 0817645489 ISBN 13: 9780817645489
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Descrizione libro Birkhäuser, 2017. Hardcover. Condizione libro: New. Never used! This item is printed on demand. Codice libro della libreria 0817645489

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## 10.An Introduction to Diophantine Equations

Editore: Springer Basel AG Sep 2010 (2010)
ISBN 10: 0817645489 ISBN 13: 9780817645489
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Descrizione libro Springer Basel AG Sep 2010, 2010. Buch. Condizione libro: Neu. Neuware - This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The material is organized in two parts: Part I introduces the reader to elementary methods necessary in solving Diophantine equations, such as the decomposition method, inequalities, the parametric method, modular arithmetic, mathematical induction, Fermat's method of infinite descent, and the method of quadratic fields; Part II contains complete solutions to all exercises in Part I. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions. An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants including Olympiad and Putnam competitors as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques. 345 pp. Englisch. Codice libro della libreria 9780817645489

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