104 Number Theory Problems muya, Teoria Liczb
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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
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104 Number Theory Problems
Titu Andreescu, Dorin Andrica, Zuming Feng
October 25, 2006
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