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Number Theory

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Algebraic (11)
Analytic (27)
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Computational (13)
Diophantine Equations (47)
Education (13)

Elliptic Curves and Modular Forms (65)
Events (200)
Factoring (51)
History (5)
Open Problems (45)
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Prime Numbers (81)
Publications (67)
Research Groups (52)
Software (56)
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Web Pages

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A Mechanical Proof of Quadratic Reciprocity - http://www.russinoff.com/papers/gauss.html
A paper by David M. Russinoff describing the use of the Boyer-Moore theorem prover in mechanically generating a proof of the Law of Quadratic Reciprocity. PS/PDF.

Active Elementary Number Theory - http://www.hbmeyer.de/taupaeng.htm
Interactive (Javascript) expression of a number as a sum of two squares.

An Introduction to the Theory of Numbers by Leo Moser - http://www.trillia.com/moser-number.html
Textbook covering following topics: compositions and partitions; arithmetic functions; distribution of primes; irrational numbers; congruences; diophantine equations; combinatorial number theory; and geometry of numbers.

Covers, Sumsets and Zero-sums - http://math.nju.edu.cn/~zwsun/csz.htm
A unified approach to covering systems, restricted sumsets and zero-sum problems by Zhi-Wei Sun.

Fermat's Little Theorem - http://www.pballew.net/FermLit.html
With notes on Carmichael numbers and the life of R.D. Carmichael.

Frequently Asked Questions - http://db.uwaterloo.ca/~alopez-o/math-faq/node21.html
Number Theory section of the sci.math FAQ list.

Hakmem Continued Fractions - http://www.inwap.com/pdp10/hbaker/hakmem/cf.html
Some notes from the MIT collection. Includes Gosper's algorithms for CF arithmetic.

Integer Relations - http://oldweb.cecm.sfu.ca/~aszanto/IntegerRelations/
To determine linear integer dependence among numerical constants and to determine the minimal polynomial of an approximate algebraic number. Interactive or via email.

Introduction to Bernoulli Numbers - http://numbers.computation.free.fr/Constants/Miscellaneous/bernoulli.html
A web article with a brief history and account of their relationship with the Riemann zeta function and Fermat's Last Theorem (HTML/PS).

Klein Polyhedra - http://keithbriggs.info/klein-polyhedra.html
Examples and algorithms for computing Klein polyhedra, also known as Arnold sails or veils (voiles), by Keith Briggs.

L-Functions - http://www.lfunctions.org/start/start.html
Classified by degree, then by level, then by eigenvalue, then by root number.

Lehmer's Conjecture - http://www.cecm.sfu.ca/~mjm/Lehmer/lc.html
That the Mahler measure of an algebraic number is bounded away from 1. Pages by Michael Mossinghoff, UCLA.

MathPages: Number Theory - http://www.mathpages.com/home/inumber.htm
Kevin Brown's collection of sci.math postings related to number theory topics.

MathWorld Number Theory - http://mathworld.wolfram.com/topics/NumberTheory.html
Index to articles in Eric Weisstein's MathWorld in the area of number theory.

Noncommutative Geometry, Trace Formulae and the Zeroes of the Riemann Zeta Function - http://www.math.ohio-state.edu/lectures/connes/Connes_course.html
Lecture notes by Alain Connes.

Number Theory - http://www.math.niu.edu/~rusin/known-math/index/11-XX.html
Dave Rusin's guide to number theory.

Number Theory - http://www.alpertron.com.ar/NUMBERT.HTM
Proofs along with equation solvers and graphical views written in Java.

Number Theory Foundation - http://www.math.uiuc.edu/ntf/
Aims to collect donations from supporters of number theory and to disburse these donations to encourage research.

Number Theory Glossary - http://www.math.umbc.edu/~campbell/NumbThy/Class/Glossary.html
Compiled by Robert Campbell.

Number Theory Web - http://www.numbertheory.org/ntw/
Things of interest to number theorists collected by Keith Matthews.

On-Line Encyclopedia of Integer Sequences - http://www.research.att.com/~njas/sequences/
Given an integer sequence, find its name, and formula.

Online Seminar: Galois theory of p-Extensions - http://public.csusm.edu/public/fhajir/kochbook.html
Email seminar on "Galoissche Theorie der p-Erweiterungen" by Helmut Koch.

Some Highlights of Arithmetic Combinatorics - http://www.math.ucla.edu/~tao/254a.1.03w/
Lecture notes and resources on combinatorial number theory by Terence Tao.

Somos Polynomials - http://grail.cba.csuohio.edu/~somos/somospol.html
Related to Somos sequences and elliptic theta functions.

Square-free Gaps - http://www.marmet.org/louis/sqfgap/index.html
Algorithm and source code for the calculation of square-free numbers and gaps.

The Arithmetic Properties of Binomial Coefficients - http://www.cecm.sfu.ca/organics/papers/granville/index.html
Activated text by Andrew Granville.

The Somos Sequence Site - http://faculty.uml.edu/jpropp/somos.html
Web resources for information on Somos sequences and related topics such as elliptic divisibility sequences.

The Valuation Theory Home Page - http://math.usask.ca/fvk/Valth.html
A forum for all mathematicians who work in valuation theory or apply valuation theoretical results in their own field of research.

The Work of Robert Langlands - http://www.sunsite.ubc.ca/DigitalMathArchive/Langlands/intro.html
Thesis, papers, manuscripts, letters and bibliography.

Transcendental Numbers - http://services.spd.dcu.ie/johnbcos/transcendental_numbers.htm
Maple worksheets, lecture notes and links to other resources by John Cosgrove.

Vignettes on Automorphic and Modular forms, Representations, L-functions, and Number Theory - http://www.math.umn.edu/~garrett/m/v/
By Paul Garrett.

World Records for Numerical Palindromes - http://www.jasondoucette.com/worldrecords.html
The 196 Palindrome Quest and The Most Delayed Palindromic Number, by Jason Doucette.

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