Shifting grounds

New states come into play as polls swing to Obama

news.bbc.co.uk

Rail strike on after talks fail

Talks aimed at averting strike action by Network Rail signalling workers break down without agreement.

news.bbc.co.uk

Smoking 'costs the NHS billions'

Smoking is costing the NHS in England £2.7bn pounds a year, up from £1.7bn a decade earlier, a report claims.

news.bbc.co.uk

Brown critic 'ends hostilities'

One of Gordon Brown's leading critics, backbench MP George Howarth, says his campaign for a Labour leadership contest is over.

news.bbc.co.uk

Fifa boss wants rules on club owners

Fifa president Sepp Blatter calls for tighter controls on wealthy foreign owners in football.

news.bbc.co.uk

New 'safer' test for Down's syndrome

Scientists develop a blood test that could tell pregnant women if their unborn baby has Down's syndrome.

news.bbc.co.uk

'Robbed'

'We lost our home to a sale and rent-back scheme'

news.bbc.co.uk

Liverpool rocked by Skrtel injury

Martin Skrtel may face a lengthy spell on the sidelines after injuring knee ligaments in Liverpool's 3-2 win at Manchester City.

news.bbc.co.uk

Smith orders police race review

Home Secretary Jacqui Smith announces a nationwide assessment of ethnic minorities in the police.

news.bbc.co.uk

Tear gas fired at mass Thai rally

Police in Thailand fire tear gas to disperse a demonstration by thousands of anti-government protesters in Bangkok.

news.bbc.co.uk

Dementia patients 'suffer stigma'

The stigma surrounding dementia makes life much harder for many patients suffering the condition, research suggests.

news.bbc.co.uk

England confident over $20m match

ECB chairman Giles Clarke says the $20m (£11.5m) match between England a Stanford Superstars XI will go ahead.

news.bbc.co.uk

Owen handed England future hope

England backroom coach Ray Clemence says Michael Owen still has an England future.

news.bbc.co.uk

Aer Lingus axes up to 1,500 jobs

Unions are to ballot for all-out industrial action as Aer Lingus announces plans to cut up to 1,500 jobs.

news.bbc.co.uk

Accused 'cooked victim's flesh'

The first winner of Mr Gay UK stabbed a man to death before cutting flesh from his thigh and trying to eat it, a court hears.

news.bbc.co.uk

Asia continues plunge in shares

Asian stocks open down sharply amid investor panic that global governments may not be able to stem the financial crisis.

news.bbc.co.uk

The human cost

'My grandfather jumped off a roof in the 1929 crash'

news.bbc.co.uk

Why this couple were delighted to have a rubbish honeymoon

A couple spent three months collecting litter around their home town to earn enough air miles to pay for part for their honeymoon.

news.bbc.co.uk

Dragon Jones heads skills academy

Dragons' Den star Peter Jones is to become head of a skills academy to teach budding entrepreneurs tricks of the trade.

news.bbc.co.uk

Send your video, pictures and story ideas

Have you got a good story? BBC News wants to hear from you.

news.bbc.co.uk

Widow forgives dead police chief

The widow of a police chief found dead days after he revealed an extra-marital affair says she has forgiven him.

news.bbc.co.uk

Prisons are in 'vicious circle'

The president of the Prison Governors Association is to warn of a "serious risk" of disturbances in jails because of a shortage of resources.

news.bbc.co.uk

Exhibit A

Your photos of the sartorial sins of your childhood

news.bbc.co.uk

Prince and Princess Michael of Kent to pay rent for royal home

Prince and Princess Michael of Kent are no longer allowed to live rent free in a Kensington Palace apartment.

news.bbc.co.uk

In the beginning

The stories that were left out of the modern-day Bible

news.bbc.co.uk

 World Catalog > Science > Math > Number Theory > Diophantine Equations

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World Catalog > Science > Math > Number Theory > Diophantine Equations

Diophantine Equations:

Bibliography on Hilbert's Tenth Problem

Searchable, 400 items.

http://liinwww.ira.uka.de/bibliography/Math/Hilbert10.html

Graand

Free Classified Ads Portal

www.graand.com

Developing A General 2nd Degree Diophantine Equation x^2 + p = 2^n

Methods to solve these equations.

http://oas.ucok.edu/OJAS/98/T98/THIENDO.HTM

Diagonal Quartic Surfaces

Articles, computations and software in Magma and GP by Martin Bright.

http://www.boojum.org.uk/maths/quartic-surfaces/

Diophantine Geometry in Characteristic p

A survey by José Felipe Voloch.

http://www.ma.utexas.edu/users/voloch/surveylatex/surveylatex.html

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.

http://www.math.hr/~duje/dtuples.html

Diophantus Quadraticus

On-line Pell Equation solver by Michael Zuker.

http://www.bioinfo.rpi.edu/~zukerm/cgi-bin/dq.html

Egyptian Fractions

Lots of information about Egyptian fractions collected by David Eppstein.

http://www.ics.uci.edu/~eppstein/numth/egypt/

The Erdos-Strauss Conjecture

The page establishes that the conjecture is true for all integers. Tables and software by Allan Swett.

http://math.uindy.edu/swett/esc.htm

Hilbert's Tenth Problem

Statement of the problem in several languages, history of the problem, bibliography and links to related WWW sites.

http://logic.pdmi.ras.ru/Hilbert10/

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.

http://www.ltn.lv/~podnieks/gt4.html

Linear Diophantine Equations

A web tool for solving Diophantine equations of the form ax + by = c.

http://www.thoralf.uwaterloo.ca/htdocs/linear.html

Pell's Equation

Record solutions.

http://www.ieeta.pt/~tos/pell.html

Pythagorean Triples Etcetera

A web text by Fred Barnes on 60-, 90-, and 120-degree integer-sided triangles.

http://www.geocities.com/fredlb37/

Pythagorean Triples in JAVA

A JavaScript applet which reads a and gives integer solutions of a^2+b^2 = c^2.

http://www.hbnweb.de/pythagoras/pythagoras.html

Pythagorean Triplets

A Javascript calculator for pythagorean triplets.

http://www.faust.fr.bw.schule.de/mhb/pythagen.htm

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.

http://www.alpertron.com.ar/QUAD.HTM

Rational and Integral Points on Higher-dimensional Varieties

Some of conjectures and open problems, compiled at AIM.

http://aimath.org/WWN/qptsurface2/

Rational Triangles

Triangles in the Euclidean plane such that all three sides are rational. With tables of Heronian and Pythagorean triples.

http://grail.cba.csuohio.edu/~somos/rattri.html

Solving General Pell Equations

John Robertson's treatise on how to solve Diophantine equations of the form x^2 - dy^2 = N.

http://hometown.aol.com/jpr2718/pelleqns.html

Thue Equations

Definition of the problem and a list of special cases that have been solved, by Clemens Heuberger.

http://finanz.math.tu-graz.ac.at/~cheub/thue.html

Rail strike on after talks fail

Talks aimed at averting strike action by Network Rail signalling workers break down without agreement.

news.bbc.co.uk

Asia continues plunge in shares

Asian stocks open down sharply amid investor panic that global governments may not be able to stem the financial crisis.

news.bbc.co.uk

Shifting grounds

New states come into play as polls swing to Obama

news.bbc.co.uk

England confident over $20m match

ECB chairman Giles Clarke says the $20m (£11.5m) match between England a Stanford Superstars XI will go ahead.

news.bbc.co.uk

Fifa boss wants rules on club owners

Fifa president Sepp Blatter calls for tighter controls on wealthy foreign owners in football.

news.bbc.co.uk

Accused 'cooked victim's flesh'

The first winner of Mr Gay UK stabbed a man to death before cutting flesh from his thigh and trying to eat it, a court hears.

news.bbc.co.uk

Owen handed England future hope

England backroom coach Ray Clemence says Michael Owen still has an England future.

news.bbc.co.uk

The human cost

'My grandfather jumped off a roof in the 1929 crash'

news.bbc.co.uk

Dementia patients 'suffer stigma'

The stigma surrounding dementia makes life much harder for many patients suffering the condition, research suggests.

news.bbc.co.uk

Widow forgives dead police chief

The widow of a police chief found dead days after he revealed an extra-marital affair says she has forgiven him.

news.bbc.co.uk

Prince and Princess Michael of Kent to pay rent for royal home

Prince and Princess Michael of Kent are no longer allowed to live rent free in a Kensington Palace apartment.

news.bbc.co.uk

Tear gas fired at mass Thai rally

Police in Thailand fire tear gas to disperse a demonstration by thousands of anti-government protesters in Bangkok.

news.bbc.co.uk

Send your video, pictures and story ideas

Have you got a good story? BBC News wants to hear from you.

news.bbc.co.uk

New 'safer' test for Down's syndrome

Scientists develop a blood test that could tell pregnant women if their unborn baby has Down's syndrome.

news.bbc.co.uk

Why this couple were delighted to have a rubbish honeymoon

A couple spent three months collecting litter around their home town to earn enough air miles to pay for part for their honeymoon.

news.bbc.co.uk

Aer Lingus axes up to 1,500 jobs

Unions are to ballot for all-out industrial action as Aer Lingus announces plans to cut up to 1,500 jobs.

news.bbc.co.uk

Exhibit A

Your photos of the sartorial sins of your childhood

news.bbc.co.uk

Prisons are in 'vicious circle'

The president of the Prison Governors Association is to warn of a "serious risk" of disturbances in jails because of a shortage of resources.

news.bbc.co.uk

Smith orders police race review

Home Secretary Jacqui Smith announces a nationwide assessment of ethnic minorities in the police.

news.bbc.co.uk

In the beginning

The stories that were left out of the modern-day Bible

news.bbc.co.uk

Liverpool rocked by Skrtel injury

Martin Skrtel may face a lengthy spell on the sidelines after injuring knee ligaments in Liverpool's 3-2 win at Manchester City.

news.bbc.co.uk

'Robbed'

'We lost our home to a sale and rent-back scheme'

news.bbc.co.uk

Smoking 'costs the NHS billions'

Smoking is costing the NHS in England £2.7bn pounds a year, up from £1.7bn a decade earlier, a report claims.

news.bbc.co.uk

Brown critic 'ends hostilities'

One of Gordon Brown's leading critics, backbench MP George Howarth, says his campaign for a Labour leadership contest is over.

news.bbc.co.uk

Dragon Jones heads skills academy

Dragons' Den star Peter Jones is to become head of a skills academy to teach budding entrepreneurs tricks of the trade.

news.bbc.co.uk