Mersenne Primes

International Year of Physics

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.

Bibliography on Hilbert's Tenth Problem http://liinwww.ira.uka.de/bibliography/Math/Hilbert10.html
Searchable, ~400 items.

Developing A General 2nd Degree Diophantine Equation x^2 + p = 2^n http://www.biochem.okstate.edu/OAS/OJAS/thiendo.htm
Methods to solve these equations.

Diagonal Quartic Surfaces http://www.boojum.org.uk/maths/quartic-surfaces/
Articles, computations and software in Magma and GP by Martin Bright.

Diophantine Equations http://www.math.niu.edu/~rusin/papers/known-math/index/11DXX.html
Dave Rusin's guide to Diophantine equations.

Diophantine Geometry in Characteristic p http://www.ma.utexas.edu/users/voloch/surveylatex/surveylatex.html
A survey by Jos� Felipe Voloch.

Diophantine m-tuples http://www.math.hr/~duje/dtuples.html
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 http://www.bioinfo.rpi.edu/~zukerm/cgi-bin/dq.html
On-line Pell Equation solver by Michael Zuker.

Egyptian Fractions http://www.ics.uci.edu/~eppstein/numth/egypt/
Lots of information about Egyptian fractions collected by David Eppstein.

Fermat's Method of Infinite Descent http://sweb.uky.edu/~jrbail01/fermat.htm
Notes by Jamie Bailey and Brian Oberg. Illustrates the method on FLT with exponent 4.

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.
On the Psixyology of Diophantine Equations http://web.inter.NL.net/hcc/J.Moree/linkind2.htm
PhD thesis, Pieter Moree, Leiden, 1993.

Pell's Equation http://www.ieeta.pt/~tos/pell.html
Record solutions.

Pythagorean Triples in JAVA http://home.foni.net/~heinzbecker/pythagoras.html
A JavaScript applet which reads a and gives integer solutions of a^2+b^2 = c^2.

Pythagorean Triplets http://www.faust.fr.bw.schule.de/mhb/pythagen.htm
A Javascript calculator for pythagorean triplets.

Quadratic Diophantine Equation Solver http://www.alpertron.com.ar/QUAD.HTM
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 http://aimath.org/WWN/qptsurface2/
Some of conjectures and open problems, compiled at AIM.

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.

computing equal sums of like powers

Computing Minimal Equal Sums Of Like Powers http://euler.free.fr/
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 http://www.glasgowg43.freeserve.co.uk/sumintro.htm
Joseph McLean's investigations into those equations.
On Equal Sums of Like Powers and Related Problems http://www.cs.man.ac.uk/cnc/EqualSums/
Classification of problems related to equal sums of like powers.
Overview of Mathematician Secret Room http://www.asahi-net.or.jp/~KC2H-MSM/mathland/overview.htm
Page keeping track of solutions of x^3+y^3+z^3 < 1000 and x^3+y^3+2*z^3 < 1000.
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.

Algebraic Geometry events

Activities in Algebraic Geometry and Related Areas http://www.math.ist.utl.pt/galg/
A list maintained at Instituto Superior T�cnico, Lisbon.

Calf http://www.maths.bath.ac.uk/~mapamk/Calf.html
UK Junior Algebraic Geometry Seminar (an offshoot of COW). Occasional meetings, mailing list.

Conferences in Algebraic Geometry and Related Fields http://www-euclid.mathematik.uni-kl.de/conferences/
A list maintained by the EAGER node at Kaiserslautern, Germany.

COW Seminar http://www.dpmms.cam.ac.uk/Seminars/COW.html
UK peripatetic algebraic geometry seminar. Programmes, mailing list, resources.

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 - G�ometrie Alg�brique En Libert� 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 Math�matiques), Luminy, Marseille, France; 21--25 March 2005.

G�om�trie Alg�brique en Libert� 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.

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