Number Theory: Structures, Examples, and Problems



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Titu Andreescu, Dorin Andrica Number Theory Str

 
About the Authors
Dorin Andrica 
received his Ph.D in 1992 from “Babe
ş
-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 Geometry Division at “Babe
ş
-Bolyai” University since 1995 and head of 
the Department of Pure Mathematics at the same University since 2007. He has 
written and contributed to numerous mathematics textbooks, problem books, 
articles and scientific papers at various levels. Dorin has been 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 one of the most important open problems in Number 
Theory”. Dorin has been a regular faculty member at the Canada–USA Mathcamps 
(2001–2005) and at the AwesomeMath Summer Program (AMSP) since 2006. 


Birkhäuser
Boston

Basel

Berlin
Titu Andreescu
Number Theory
Structures, Examples, and Problems
Dorin Andrica


Titu Andreescu
University of Texas at Dallas
2601 N. Floyd Road, FN 33
Richardson, TX 75002, USA
titu.andreescu@utdallas.edu
Dorin Andrica
and Computer Science
Faculty of Mathematics 
“Babe -Bolyai” University
Str. Kogalniceanu 1
3400 Cluj-Napoca, Romania
dandrica@math.ubbcluj.ro
Printed on acid-free paper.
www.birkhauser.com
and Mathematics Education
ISBN: 978-0-8176-3245-8
e-ISBN: 978-0-8176-4645-5
DOI: 10.1007/b11856
Library of Congress Control Number: 2009921128
All rights reserved. This work may not be translated or copied in whole or in part without the writ-
ten permission of the publisher (Birkhäuser 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.
©
Birkhäuser Boston, a part of Springer Science
+
Business Media, LLC 2009
Mathematics Subject Classification (2000): 11A05, 11A07, 11A15, 11A25, 11A25, 11B37, 11B39,
Cover Design by Joseph Sherman
Department of Science
ş
11B65, 11D04, 11D09, 11D25


Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk.
God made the integers, all else is the work of man.
Leopold Kronecker




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