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Mersenne Primes

1, 3, 8, 120, ...
Sets of numbers such that the product of any two is one less than a square. Diophantus found the rational set 1/16, 33/16, 17/4, 105/16; Fermat the integer set 1, 3, 8, 120.
Bibliography on Hilbert's Tenth Problem
Searchable, ~400 items.
Developing A General 2nd Degree Diophantine Equation x^2 + p = 2^n
Methods to solve these equations.
Diagonal Quartic Surfaces
Articles, computations and software in Magma and GP by Martin Bright.
Diophantine Equations
Dave Rusin's guide to Diophantine equations.

Diophantine Geometry in Characteristic p
A survey by José Felipe Voloch.
Diophantine m-tuples
Sets with the property that the product of any two distinct elements is one less than a square. Notes and bibliography by Andrej Dujella.
Diophantus Quadraticus
On-line Pell Equation solver by Michael Zuker.
Egyptian Fractions
Lots of information about Egyptian fractions collected by David Eppstein.
Fermat's Method of Infinite Descent
Notes by Jamie Bailey and Brian Oberg. Illustrates the method on FLT with exponent 4.

Hilbert's Tenth Problem
Given a Diophantine equation with any number of unknowns and with rational integer coefficients: devise a process, which could determine by a finite number of operations whether the equation is solvable in rational integers.
Hilbert's Tenth Problem
Statement of the problem in several languages, history of the problem, bibliography and links to related WWW sites.
Linear Diophantine Equations
A web tool for solving Diophantine equations of the form ax + by = c.
MAGMA program
MAGMA code to solve Diophantine equations of the form F(x)=G(y), for which Runge's condition is satisfied. Created by Szabolcs Tengely.
On the Psixyology of Diophantine Equations
PhD thesis, Pieter Moree, Leiden, 1993.

Pell's Equation
Record solutions.
Pythagorean Triples in JAVA
A JavaScript applet which reads a and gives integer solutions of a^2+b^2 = c^2.
Pythagorean Triplets
A Javascript calculator for pythagorean triplets.
Quadratic Diophantine Equation Solver
Dario Alpern's Java/JavaScript code that solves Diophantine equations of the form Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0 in two selectable modes: "solution only" and "step by step" (or "teach") mode. There is also a link to his description of the solving methods.
Rational and Integral Points on Higher-dimensional Varieties
Some of conjectures and open problems, compiled at AIM.

Rational Triangles
Triangles in the Euclidean plane such that all three sides are rational. With tables of Heronian and Pythagorean triples.
Solving General Pell Equations
John Robertson's treatise on how to solve Diophantine equations of the form x^2 - dy^2 = N.
The Erdos-Strauss Conjecture
The conjecture states that for any integer n > 1 there are integers a, b, and c with 4/n = 1/a + 1/b + 1/c, a > 0, b > 0, c > 0. The page establishes that the conjecture is true for all integers n, 1 < n <= 10^14. Tables and software by Allan Swett.
Thue Equations
Definition of the problem and a list of special cases that have been solved, by Clemens Heuberger.

computing equal sums of like powers

Computing Minimal Equal Sums Of Like Powers
Jean-Charles Meyrignac's distributed-computing project on equal sums of like powers and the place to look for the current status of the problem.
Equations Involving Sums of Powers
Joseph McLean's investigations into those equations.
On Equal Sums of Like Powers and Related Problems
Classification of problems related to equal sums of like powers.
Overview of Mathematician Secret Room
Page keeping track of solutions of x^3+y^3+z^3 < 1000 and x^3+y^3+2*z^3 < 1000.
Power Page
Steve Dutch's page about powers of numbers.

D. J. Bernstein's collection of tools for enumerating small solutions to certain types of equal sums of like powers.
Taxicab Numbers
David W. Wilson's list of the smallest number that can be expressed as a sum of two positive cubes in n different ways, for n = 1 through 5.
The Fifth Taxicab Number is 48988659276962496
David W. Wilson's article on his search for the smallest integer that can be expressed as a sum of two positive cubes in 5 distinct ways, up to order of summands.
Tom's Mathematical Things
Dissertation about equal sums of like powers by Tom Womack.

Algebraic Geometry events

Activities in Algebraic Geometry and Related Areas
A list maintained at Instituto Superior Técnico, Lisbon.

UK Junior Algebraic Geometry Seminar (an offshoot of COW). Occasional meetings, mailing list.

Conferences in Algebraic Geometry and Related Fields
A list maintained by the EAGER node at Kaiserslautern, Germany.

COW Seminar
UK peripatetic algebraic geometry seminar. Programmes, mailing list, resources.

EAGER Activities
European Algebraic Geometry Research Training Network. Activities of or related to the network.

Equivariant Intersection Theory
28th Autumn School in Algebraic Geometry. Lukecin, Poland; 11--17 September 2005.

GAEL - Géometrie Algébrique En Liberté
A series of conferences particularly designed for researchers in Algebraic Geometry at the beginning of their scientific career.

CIRM (Centre International de Rencontres Mathématiques), Luminy, Marseille, France; 21--25 March 2005.

Géométrie Algébrique en Liberté
A series of conferences aimed at researchers in Algebraic Geometry at the beginning of their scientific career.

MEGA 2005
The Eighth International Symposium on Effective Methods in Algebraic Geometry. Computing in and with algebraic geometry: Theory, Algorithms, Implementations, Applications. Porto Conte, Alghero, Sardinia,Italy; 26 May -- 2 June 2005.

Summer Institute in Algebraic Geometry
Three one-week sessions: Interactions with physics; Classical geometry; Arithmetic geometry. University of Washington, Seattle, WA, USA; 25 July -- 12 August 2005.

Trento Schools
Intended for European doctoral students and post-doctoral fellows in algebraic geometry.

VBAC Meetings
Past and future meetings on Vector Bundles on Algebraic Curves.

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