1, 3, 8, 120, ... - http://www.weburbia.demon.co.uk/pg/diophant.htm 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.
Hilbert's Tenth Problem - http://www.ltn.lv/~podnieks/gt4.html 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 - http://logic.pdmi.ras.ru/Hilbert10/ Statement of the problem in several languages, history of the problem, bibliography and links to related WWW sites.
Linear Diophantine Equations - http://www.thoralf.uwaterloo.ca/htdocs/linear.html A web tool for solving Diophantine equations of the form ax + by = c.
MAGMA program - http://www.math.leidenuniv.nl/~tengely/main2.html MAGMA code to solve Diophantine equations of the form F(x)=G(y), for which Runge's condition is satisfied. Created by Szabolcs Tengely.
Rational Triangles - http://grail.cba.csuohio.edu/~somos/rattri.html Triangles in the Euclidean plane such that all three sides are rational. With tables of Heronian and Pythagorean triples.
Solving General Pell Equations - http://hometown.aol.com/jpr2718/pelleqns.html John Robertson's treatise on how to solve Diophantine equations of the form x^2 - dy^2 = N.
The Erdos-Strauss Conjecture - http://math.uindy.edu/swett/esc.htm 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 - http://finanz.math.tu-graz.ac.at/~cheub/thue.html Definition of the problem and a list of special cases that have been solved, by Clemens Heuberger.
Power Page - http://www.uwgb.edu/dutchs/RECMATH/rmpowers.htm Steve Dutch's page about powers of numbers.
Sortedsums - http://cr.yp.to/sortedsums.html D. J. Bernstein's collection of tools for enumerating small solutions to certain types of equal sums of like powers.
Taxicab Numbers - http://pi.lacim.uqam.ca/eng/problem_en.html 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 - http://www.cs.uwaterloo.ca/journals/JIS/wilson10.html 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 - http://tom.womack.net/maths/dissert_abstract.htm Dissertation about equal sums of like powers by Tom Womack.
EAGER Activities - http://euclid.mathematik.uni-kl.de/activities/ European Algebraic Geometry Research Training Network. Activities of or related to the network.
Equivariant Intersection Theory - http://www.mimuw.edu.pl/~alan/html/Lukecin05.html 28th Autumn School in Algebraic Geometry. Lukecin, Poland; 11--17 September 2005.
GAEL - Géometrie Algébrique En Liberté - http://euclid.mathematik.uni-kl.de/~gael/ A series of conferences particularly designed for researchers in Algebraic Geometry at the beginning of their scientific career.
GAEL XIII - http://www-euclid.mathematik.uni-kl.de/~gael/GaelXIII/GaelXIII.html CIRM (Centre International de Rencontres Mathématiques), Luminy, Marseille, France; 21--25 March 2005.
Géométrie Algébrique en Liberté - http://www-euclid.mathematik.uni-kl.de/~gael/ A series of conferences aimed at researchers in Algebraic Geometry at the beginning of their scientific career.
MEGA 2005 - http://www.dm.unipi.it/MEGA05/ 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 - http://www.math.princeton.edu/~rahulp/seattle05.html Three one-week sessions: Interactions with physics; Classical geometry; Arithmetic geometry. University of Washington, Seattle, WA, USA; 25 July -- 12 August 2005.
Trento Schools - http://euclid.mathematik.uni-kl.de/activities/trento.html Intended for European doctoral students and post-doctoral fellows in algebraic geometry.
VBAC Meetings - http://www.mi.uni-erlangen.de/~forkel/vbac/meetings.html Past and future meetings on Vector Bundles on Algebraic Curves.