A Mechanical Proof of Quadratic Reciprocity
- 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.
- http://www.russinoff.com/papers/gauss.html

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

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

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

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

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

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

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

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

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

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

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

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

Linear Independence Measures for Logarithms of Algebraic Numbers
- Michel Waldschmidt. Cetraro summer school lectures, July 2000.
- http://www.mathp6.jussieu.fr/~miw/articles/cetraro.html

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

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

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

Infinite Series Theorem
- Addresses the question whether a series of rational functions converges to a rational number.
- http://www.infiniteseriestheorem.org/

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

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

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

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

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

L-Functions
- Classified by degree, then by level, then by eigenvalue, then by root number.
- http://www.math.okstate.edu/~loriw/start/start.html

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

Some Number-Theoretical Constants
- Products of rational functions of p over primes, computed by Gerhard Niklasch and Pieter Moree.
- http://www.gn-50uma.de/alula/essays/Moree/Moree.en.shtml

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

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

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

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

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

The Somos Sequence Site
- Web resources for information on Somos sequences and related topics such as elliptic divisibility sequences.
- http://www.math.wisc.edu/~propp/somos.html

Visible Structures in Number Theory
- By Peter Borwein and Loki Jörgenson. Recognising number patterns visually.
- http://www.cecm.sfu.ca/~loki/Papers/Numbers/