21. Pell Worked on algebra and number theory, gave a table of factors of all integers up to 100000 in 1668. Pell's equation is y^2 = ax^2 + 1, where a is a nonsquare integer. http://history.math.csusb.edu/Mathematicians/Pell.html

John Pell Born: 1 March 1611 in Southwick, Sussex, England Died: 12 Dec 1685 in London, England Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index After attending Steyning School in Sussex, John Pell entered Trinity College, Cambridge in 1624. He received his B.A. in 1628 and his M.A. in 1630. After leaving Cambridge, Pell became a schoolmaster. He worked first in Horsham, then in Chichester. He spent five years from 1638 teaching mathematics in London. He then went abroad becoming Professor of Mathematics at a College in Amsterdam from 1643 until he took up a similar post the University of Breda in 1646. Pell returned to England in 1652 and was appointed by Oliver Cromwell to a post teaching mathematics in London. He spent the years 1654 to 1658 holding a government post in Zurich. On his return to England became a vicar and remained in this position in the church for the last 20 years of his life. Pell worked on algebra and number theory . He gave a table of factors of all integers up to 100000 in 1668. Pell's equation y ax + 1, where a is a non-square integer, was first studied by

22. Journal Of Number Theory The Journal of number theory was founded at The Ohio State University in 1969 by Professors RP Bambah, P. Roquette, A. Ross, A. Woods, and H. Zassenhaus. http://www.math.ohio-state.edu/JNT/

The Journal of Number Theory was founded at The Ohio State University in 1969 by Professors R.P. Bambah, P. Roquette, A. Ross, A. Woods, and H. Zassenhaus. Editor-in-Chief: David Goss Managing Editor: Ranko Bojanic For more information, including a list of editorial board members and author instructions, please see Elsevier Office Susan Hunter Department of Mathematics The Ohio State University 231 West 18th Avenue Columbus, Ohio 43210-1174 Phone: (614) 292-7670 Email: jnt@math.ohio-state.edu

23. Magma Computational Algebra System Home Page Comprehensive system for algebra, number theory and geometry. Can work with polynomials, matrices, groups, rings, fields, modules, lattices, algebras, graphs, codes, and curves. http://www.maths.usyd.edu.au:8000/u/magma/

The Magma Computational Algebra System for Algebra, Number Theory and Geometry Magma is a large, well-supported software package designed to solve computationally hard problems in algebra, number theory, geometry and combinatorics. It provides a mathematically rigorous environment for computing with algebraic, number-theoretic, combinatoric and geometric objects. Recent Notices: May 31, 2004: Magma version V2.11 has now been released. Registered users may now download V2.11 for Mac (OS X), PC (Linux) and Sparc (Solaris) from here here for example timings. About Magma What's New Magma on-line help FAQ ... Online Magma Calculator (external link) Magma is produced and distributed by the Computational Algebra Group within the School of Mathematics and Statistics of the University of Sydney.

24. Inexplicable Secrets Of Creation Relationships between number theory and physics. http://www.maths.ex.ac.uk/~mwatkins/

"Upon looking at these numbers, one has the feeling of being in the presence of one of the inexplicable secrets of creation [D. Zagier] mysterious occurrences on the interface of physics and number theory introductory prime number theory resources related curiosities guest book ... a message about the future of this website

25. Springer-Verlag - Number Theory & Combinatorics Neal Koblitz. An algorithmic approach that covers basic arithmetic topics all the way to elliptic curves. http://www.springer-ny.com/detail.tpl?isbn=0387942939

26. Number Theory Glossary number theory Glossary. Abelian Group An abelian group is a group whose operation is commutative, ie a * b = b * a . An example of http://www.math.umbc.edu/~campbell/NumbThy/Class/Glossary.html

Number Theory Glossary Abelian Group An abelian group is a group whose operation is commutative, ie a b b a . An example of an abelian group is the integers with the usual addition operation. An example of a group which is not abelian is the rotations of a cube (try it out). When dealing with an abelian group is it conventional to denote the group operation as addition (+), rather than multiplication (*) and to denote the unit element as rather than 1. Carmichael Number A Carmichael Number is a composite number which passes the Fermat pseudoprime test for all bases. There are an infinite number of Carmichael numbers - the smallest is 561=11*17*3. Composite A composite number has non-trivial factors (ie factors other than itself and 1). Thus 13 is prime but 15=3*5 is composite. A number which is not composite is called prime . A polynomial which has non-trivial factors is called reducible Euler Pseudoprime Test A more effective pseudoprime test than the simpler Fermat test . A number N is called an Euler pseudoprime to base b if b N b N ) (mod N ). (Here (

27. Mathematics Archives MSDOS Software For Number Theory Math Archives Homepage Windows/MSDos Software Collection for number theory. The following icons indicate the type of package Freeware or Public Domain. http://archives.math.utk.edu/software/msdos/number.theory/.html

Windows/MSDos Software Collection for Number Theory The following icons indicate the type of package: Freeware or Public Domain Shareware with all features enabled Shareware with some features disabled Commercial Software Demo of Commercial Software List of Packages Aliquot Calc GP-PARI for DOS and OS/2 MPQSHD prime factorization program Malm - a collection of UBASIC programs NUMBERS calculator UBASIC This collection is maintained by Larry Husch . If you know of any Windows/MSDOS programs which are not listed in this collection and which you think are useful in the teaching of mathematics, then write Larry You are invited to submit materials to be stored on the Mathematics Archives; this may include software, reviews of software or teaching materials utilizing technology. For more information on uploading materials, read this

28. Pushpa Publishing House, Allahabad, Uttar Pradesh India (Pushpa) Table of contents and abstracts from vol.1 (2001). http://www.pphmj.com/jpanjournals.htm

Vijaya Niwas, 198 Mumfordganj Allahabad - 211002, India arun@pphmj.com The Pushpa Publishing House announces (i) Volume 14(2004) and Volume 17(2004) of the Far East Journal of Applied Mathematics as the Special Volumes devoted largely to the articles concerned with the Applications of Numerical Methods in the Partial Differential Equations, Fluid Mechanics, Magnetohydrodynamics, and other related topics. (ii) Volume 13(2004) of the Far East Journal of Theoretical Statistics as the Special Volume devoted largely to the articles concerned with the Biostatistics and other related topics. The JP Journal of Algebra, Number Theory and Applications is published in three issues per volume annually appearing in April, August and December. Original research papers and critical survey articles in areas of current interest in Algebra, Number Theory and their Applications are considered for publication. Reviewed: Mathematical Reviews and Zentralblatt fur Mathematik.

29. NTL: A Library For Doing Number Theory NTL A Library for doing number theory. NTL is a highperformance, portable C++ library providing data structures and algorithms http://www.shoup.net/ntl/

NTL: A Library for doing Number Theory NTL is a high-performance, portable C++ library providing data structures and algorithms for manipulating signed, arbitrary length integers, and for vectors, matrices, and polynomials over the integers and over finite fields. A Tour of NTL Download NTL Trouble-shooting guide Contact Info and Mailing Lists ... Related Links Now available: NTL 5.3.2 [More detailed information about recent changes] Back to Victor Shoup's Home Page

30. Welcome To The Homepage Of The Computer Algebra Research Group Of The IWR Computer Algebra research group of the IWR, Heidelberg. People, research, teaching, activities, software and links. http://www.iwr.uni-heidelberg.de/groups/compalg/

ALGORITHMIC ALGEBRA AND NUMBER THEORY Research group Prof. Dr. B.H. Matzat IWR Im Neuenheimer Feld 368 D-69120 Heidelberg Germany Tel: +49 6221 54-8318 Fax: +49 6221 54-8850 People Research Teaching Activities ... michael.dettweiler@IWR.uni-heidelberg.de

31. A Computational Introduction To Number Theory And Algebra A Computational Introduction to number theory and Algebra. A preliminary version of a book introducing basic concepts from computational http://www.shoup.net/ntb/

A Computational Introduction to Number Theory and Algebra A preliminary version of a book introducing basic concepts from computational number theory and algebra, including all the necessary mathematical background. Now available: BETA version 3 This is a major revision of BETA version 2, with a number of bug fixes and lots of polishing. The book is now essentially in final form. Dowload PDF files Front Matter (102KB): title page, preface, table of contents Book (BETA version 3, 488 pages, 2.803MB) Back to Victor Shoup's Home Page

32. NUMBER THEORY WEB (UK SITE) number theory Web. (UK Site). http://www.dpmms.cam.ac.uk/Number-Theory-Web/

Number Theory Web (UK Site) Aims New Listings Number theorists' Home Pages/Departmental listings Things of Interest to Number Theorists ... Search the Number Theory Web Pages in Cambridge, UK This site is a mirror of the Australian site at Brisbane, Australia The main site is now in Vancouver, as of 31st May 2003 The Italian mirror site Francesco Pappalardi The Japanese mirror site is at the University of Electro-Communication, Tokyo (courtesy of Masanari Kida The Indian mirror site is at the Harish-Chandra Research Institute, Allahabad (courtesy of Shripad Garge Maintained by Keith Matthews , Dept of Math, University of Queensland, Brisbane, Australia Suggestions for additions or improvements are welcome. Contact me by email at krm@maths.uq.edu.au This page last modified 2nd June 2003

33. Number Theory number theory. This site features Generic Two integer variable equation solver Diophantine equation ax 2 + bxy + cy 2 + dx + ey http://www.alpertron.com.ar/NUMBERT.HTM

Dario Alpern's site Home Page Ver sitio en castellano ELECTRONICS Intel Microprocessors (Spanish only) MATHEMATICS Calculators Number Theory Problems PROGRAMS Assembler 80386 (downloads) Java Games CONTACT Personal Comments Guestbook Discussion board ... Donations Number theory This site features: Generic Two integer variable equation solver Diophantine equation ax + bxy + cy + dx + ey + f = solver, where the unknowns x and y can be integer numbers only. Written in Java/JavaScript. Last updated on May 31st, 2001. Quadratic modular equation solver Calculator that can solve equations of the form ax + bx + c = (mod n) . Last updated: May 2nd, 2002. Sum of powers Table of relations of the form a p + b q = c r with gcd(a,b,c) = 1 . Last updated: September 7th, 2003. Ulam's Spiral Java applet featuring a graphical view of prime numbers. Last updated on February 14th, 2003. Factorization using the Elliptic Curve Method Applet that can be used to find 20- or 30-digit factors of numbers or numerical expressions up to 1000 digits long. It also computes the number and sum of divisors, Euler's totient and Moebius, and its decomposition as a sum of up to 4 perfect squares. Last updated on February 9th, 2003. Gaussian Integer Factorization applet Finds the factors of complex numbers of the form a+bi where a and b are integers. It also includes a complete calculator with operators and functions using gaussian integers. Last updated on June 1st, 2002.

34. Euclid's Elements, Introduction Includes the entire 13 books on plane geometry, geometric and abstract algebra, number theory, incommensurables, and solid geometry. Uses java applets to illustrate the principles. http://aleph0.clarku.edu/~djoyce/java/elements/elements.html

Introduction New: Jaume Domenech Larraz has translated the Elements into Catalan at http://www.euclides.org/ Euclid's Elements form one of the most beautiful and influential works of science in the history of humankind. Its beauty lies in its logical development of geometry and other branches of mathematics. It has influenced all branches of science but none so much as mathematics and the exact sciences. The Elements have been studied 24 centuries in many languages starting, of course, in the original Greek, then in Arabic, Latin, and many modern languages. I'm creating this version of Euclid's Elements for a couple of reasons. The main one is to rekindle an interest in the Elements, and the web is a great way to do that. Another reason is to show how Java applets can be used to illustrate geometry. That also helps to bring the Elements alive. The text of all 13 Books is complete, and all of the figures are illustrated using the Geometry Applet, even those in the last three books on solid geometry that are three-dimensional. I still have a lot to write in the guide sections and that will keep me busy for quite a while. This edition of Euclid's Elements uses a Java applet called the Geometry Applet to illustrate the diagrams. If you enable Java on your browser, then you'll be able to dynamically change the diagrams. In order to see how, please read

35. Perfectly Scientific - Home the scientific algorithm company. Experts in compression, wavelets, FFT, general transforms, color graphics, Monte Carlo, fractals, convolution,signal processing, matrix algebra, genetic algorithms, number theory. http://www.perfsci.com/

PSI news New largest prime number! We have a physical poster . The prime is , discovered in May 2004. Newly free software PSI offers unique services that are hard to find elsewhere. We specialize in industrial algorithm problems. Contact us to help solve your specific algorithm problems. PSI offers software that embodies classical algorithms and/or our proprietary algorithms. As for hardware, PSI designs and supports laboratory peripherals for Mac OS X. See our software and hardware page PSI also provides a unique collection of scientific souvenir and gifts.

36. INTEGERS: The Electronic Journal Of Combinatorial Number Theory INTEGERS is a refereed electronic journal devoted to research in the area of combinatorial number theory. It is published with the http://www.integers-ejcnt.org/

INTEGERS is a refereed electronic journal devoted to research in the area of combinatorial number theory. It is published with the help of the State University of West Georgia, Charles University, and DIMATIA. Subscriptions to INTEGERS are free. We welcome original research articles in combinatorics and number theory, with a preference for those that have a connection to both fields. Topics covered by the journal include additive number theory, multiplicative number theory, sequences and sets, extremal combinatorics, Ramsey theory, elementary number theory, classical combinatorial problems, hypergraphs, and probabilistic number theory. The principal subject areas, according to the American Mathematical Society subject classification scheme are 05A, 05C55, 05C65, 05D, 11A, 11B, 11K, 11N, 11P, 11Y, and 91A46. INTEGERS houses a Combinatorial Games section. Current Volume Previous Volumes Editorial Board How to Submit a Paper ... Download Statistics Home

37. Lessons On Number Theory From Math Goodies Math Goodies offers 7 interactive lessons on topics number theory including factors, multiples, primes, composites, divisibility, and exponents. http://www.mathgoodies.com/lessons/toc_vol3.shtm

interactive click here fun Lessons CD Forums Homework ... Newsletter numbers Advertise Recommend Puzzles About Us ... Articles Our interactive lessons are in-depth learning modules that provide detailed examples, diagrams, summaries and exercises. Each volume of lessons consists of a related group of lessons, practice exercises, challenge exercises, and a solutions page. Read the Terms and Conditions for using our free demo lessons. First time users also need to read this Important Information Lesson Description Factors and Greatest Common Factors To define factor and greatest common factor (GCF). To learn the procedure for finding all factors of a whole number. To learn the procedure for finding the GCF of two or more whole numbers. Multiples and Least Common Multiples To define multiple and least common multiple (LCM). To learn the procedure for finding the multiples of a whole number. To learn the procedure for finding the LCM of two or more whole numbers. Available on CD only Prime and Composite Numbers To define prime and composite numbers. To determine if a number is prime or composite by examining its factors.

38. Nicholas M. Katz's Home Page Professor of number theory Algebraic Geometry, Princeton University. Space filling curves over finite fields. http://www.math.princeton.edu/~nmk

Check out monodromy.com Bibliography of Nicholas M. Katz pdf file (70 KB) C.V. of Nicholas M. Katz pdf file (6 KB) Photo from 60'th Birthday Conference jpg file (807 KB) Photo from 60'th Birthday Conference (high resolution version) TIF file (123 MB) Nicholas M. Katz PDF and DVI files available for download On a question of Lillian Pierce dvi file (44 KB) pdf file (982 KB) Hooley parameters for families of exponential sums over finite fields pdf file Notes on G_2, determinants, and equidistribution (typo's corrected Dec. 9, 2003) pdf file online version (joint with Esnault) Cohomological divisibility and point count divisibility (corrected version of nov. 10, 2003) dvi file (41 KB) pdf file (187 KB) Corrected version of Chapter 5 of "Twisted L-Functions and Monodromy" pdf file (Annals of Math Study, to appear) Moments, Monodromy, and Perversity: a Diophantine Perspective Corrections to "Space filling curves over finite fields" dvi file (12 KB) pdf file (88 KB) (joint with Pandharipande) Inequalities related to Lefschetz pencils and integrals of Chern classes pdf file (80 KB) Estimates for "nonsingular" multiplicative character sums dvi file (60 KB) pdf file (206 KB) A semicontinuity result for monodromy under degeneration dvi file (36 KB) pdf file (163 KB) Sato-Tate Equidistribution of Kurlberg-Rudnick Sums pdf file (94 KB) AWS2000 Lectures: L -functions and monodromy: four lectures on Weil II pdf file (184 KB) Larsen's Alternative, Moments, and the Monodromy of Lefschetz Pencils

39. Introduction To Number Theory next contents Next Contents. amssym.def. Introduction to number theory. XD JIA. SOUTHWEST TEXAS STATE UNIVERSITY Spring 1996. Contents; http://www.math.swt.edu/~haz/prob_sets/notes/notes.html

Next: Contents amssym.def Introduction to Number Theory X.-D. J IA S OUTHWEST T EXAS S TATE U NIVERSITY Spring 1996 Contents The Factorization of Integers Divisibility Prime Numbers ... Euler -Function Congruences Chinese Remainder Theorem Congruences Modulo a Prime Power Quadratic Residues ... About this document ... Donald Hazlewood and Carol Hazlewood Wed Jun 5 14:35:14 CDT 1996

40. NUMBER THEORY CONFERENCES, NEW AND OLD Part of the number theory Web, compiled by Keith Matthews. http://www.maths.uq.edu.au/~krm/N3.html

Number Theory Conferences, new and old Rational and integral points on higher-dimensional varieties , January 9 - May 19, 2006, MSRI, Berkeley, California 2004 West Coast Number Theory Conference , December 16-20, 2004 National Conference on Discrete Mathematics and its Applications , December 9-11, 2004, Amrita Vishwa Vidyapeetham University Diophantine approximation and analytic number theory , 20-25 November 2004, Banff Explicit methods in number theory , 13-18 November 2004, Banff Number Theoretic Algorithms and Related Topics , Sept 27-Oct 1, 2004, Strobl, Austria Workshop on Elliptic Curve Cryptography Workshop on harmonic analysis and number theory , September 18-20, 2004, University of Exeter Explicit Methods in Number Theory Special session on Analytic Number Theory , August 17-19, 2004, 6th WSEAS conference on Applied Mathematics, Greece Bunyakovsky International Conference , August 16-21, 2004, Kiev Summer school: Modular forms and their applications , August 16-20, 2004, Sophus Lie Conference Center, Nordfjordeid, Norway Number Theory Conference in honour of Harold Stark , August 5-7, 2004, University of Minnesota, Minneapolis ALTENCOA 2004 , July 19-23, 2004, Universidad de Antioquia, Colombia Matrix Ensembles and L-Functions , July 12-16, 2004, Newton Institute, Cambridge UK From Arithmetic to Cryptology , a conference on the occasion of Gerhard Frey's 60th birthday, July 8-10, 2004, University of Duisburg-Essen, Essen Campus, Germany Summer school on the geometry and arithmetic of algebraic curves , July 5-16, 2004, Beirut, Lebanon (

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