Andreescu et al. - 104 Number Theory Problems (2007).pdf - Number Theory - Mathematics2014

About the Authors

Titu Andreescu received his Ph.D. from the West University of Timisoara, Ro-

mania. The topic of his dissertation was “Research on Diophantine Analysis and

Applications.” Professor Andreescu currently teaches at The University of Texas

at Dallas. He is past chairman of the USA Mathematical Olympiad, served as di-

rector of the MAA American Mathematics Competitions (1998–2003), coach of

the USA International Mathematical Olympiad Team (IMO) for 10 years (1993–

2002), director of the Mathematical Olympiad Summer Program (1995–2002),

and leader of the USA IMO Team (1995–2002). In 2002 Titu was elected member

of the IMO Advisory Board, the governing body of the world’s most prestigious

mathematics competition. Titu co-founded in 2006 and continues as director of

the AwesomeMath Summer Program (AMSP). He received the Edyth May Sliffe

Award for Distinguished High School Mathematics Teaching from the MAA in

1994 and a “Certiﬁcate of Appreciation” from the president of the MAA in 1995

for his outstanding service as coach of the Mathematical Olympiad Summer Pro-

gram in preparing the US team for its perfect performance in Hong Kong at the

1994 IMO. Titu’s contributions to numerous textbooks and problem books are

recognized worldwide.

Dorin Andrica received his Ph.D in 1992 from “Babe¸-Bolyai” University in

Cluj-Napoca, Romania; his thesis treated critical points and applications to the

geometry of differentiable submanifolds. Professor Andrica has been chairman of

the Department of Geometry at “Babe¸-Bolyai” since 1995. He has written and

contributed to numerous mathematics textbooks, problem books, articles and sci-

entiﬁc papers at various levels. He is an invited lecturer at university conferences

around the world: Austria, Bulgaria, Czech Republic, Egypt, France, Germany,

Greece, Italy, the Netherlands, Portugal, Serbia, Turkey, and the USA. Dorin is

a member of the Romanian Committee for the Mathematics Olympiad and is a

member on the editorial boards of several international journals. Also, he is well

known for his conjecture about consecutive primes called “Andrica’s Conjecture.”

He has been a regular faculty member at the Canada–USA Mathcamps between

2001–2005 and at the AwesomeMath Summer Program (AMSP) since 2006.

Zuming Feng received his Ph.D. from Johns Hopkins University with emphasis

on Algebraic Number Theory and Elliptic Curves. He teaches at Phillips Exeter

Academy. Zuming also served as a coach of the USA IMO team (1997–2006), was

the deputy leader of the USA IMO Team (2000–2002), and an assistant director of

the USA Mathematical Olympiad Summer Program (1999–2002). He has been a

member of the USA Mathematical Olympiad Committee since 1999, and has been

the leader of the USA IMO team and the academic director of the USA Mathe-

matical Olympiad Summer Program since 2003. Zuming is also co-founder and

academic director of the AwesomeMath Summer Program (AMSP) since 2006.

He received the Edyth May Sliffe Award for Distinguished High School Mathe-

matics Teaching from the MAA in 1996 and 2002.

Titu Andreescu

Dorin Andrica

Zuming Feng

104 Number Theory

Problems

From the Training of the USA IMO Team

Birkhauser

Boston • Basel • Berlin

Titu Andreescu

The University of Texas at Dallas

Department of Science/Mathematics Education

Richardson, TX 75083

U.S.A.

titu.andreescu@utdallas.edu

Dorin Andrica

“Babe¸-Bolyai” University

Faculty of Mathematics

3400 Cluj-Napoca

Romania

dorinandrica@yahoo.com

Zuming Feng

Phillips Exeter Academy

Department of Mathematics

Exeter, NH 03833

U.S.A.

zfeng@exeter.edu

Cover design by Mary Burgess.

Mathematics Subject Classiﬁcation (2000): 00A05, 00A07, 11-00, 11-XX, 11Axx, 11Bxx, 11D04

Library of Congress Control Number: 2006935812

ISBN-10: 0-8176-4527-6

e-ISBN-10: 0-8176-4561-6

ISBN-13: 978-0-8176-4527-4

e-ISBN-13: 978-0-8176-4561-8

Printed on acid-free paper.

2007 Birkhauser Boston

ten permission of the publisher (Birkhauser Boston, c/o Springer Science

Business Media LLC, 233

Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or

scholarly analysis. Use in connection with any form of information storage and retrieval, electronic

adaptation, computer software, or by similar or dissimilar methodology now known or hereafter de-

veloped is forbidden.

The use in this publication of trade names, trademarks, service marks and similar terms, even if they

are not identiﬁed as such, is not to be taken as an expression of opinion as to whether or not they are

subject to proprietary rights.

987654321

www.birkhauser.com

(EB)

104 Number Theory Problems

Titu Andreescu, Dorin Andrica, Zuming Feng

October 25, 2006

Andreescu et al. - 104 Number Theory Problems (2007).pdf

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