New light on BHASKARA'S CHAKRAVALA or cyclic method of solving indeterminate equations of the second degree in two variables. The first complete proof of Bhaskara's Cyclic Method is sketched in this paper.

Avinash Sathaye Visit Indology related sites for other interests.

<http://www.ms.uky.edu/~sohum/AAK/PRELUDE.htm>

Bhaskara II

WikipÃ©dia

<http://fr.wikipedia.org/wiki/Bhaskara_II>

Equation de Pell-Fermat et groupe sur une hyperbole

Cette page trouve - elle aussi - son origine dans le sujet de CAPES interne 1991. Dans la premiÃ¨re partie de ce sujet, on cherche Ã rÃ©soudre dans Z l'Ã©quation x2 - 3y2 = 1. La suite est Ã prendre comme une simple illustration graphique de cette partie.

<http://www-cabri.imag.fr/abracadabri/Algebre/PellFermat/HypPF.html>

Pell's equation

J J O'Connor and E F Robertson

References for: Pell's equation

<http://turnbull.dcs.st-and.ac.uk/~history/HistTopics/Pell.html>

ALGORITHMES

pell equation's solution by continue fraction method

Hisanori Mishima

<http://www.asahi-net.or.jp/~KC2H-MSM/mathland/math08/math0803.htm>

DEMOS

Pell Equation solver X^2 - dY^2 = +/- 1

<http://bioinfo.math.rpi.edu/~zukerm/cgi-bin/dq.html>

OUTILS - TOOLS

Equation de PELL - FERMAT

Il s'agit de rÃ©soudre dans l'ensemble des entiers l'Ã©quation : x² - Ny² = 1 OÃ¹ N est un entier donnÃ© par l'utilisateur.

J.F.Heintzen ac.orleans-tours.fr

<http://www.ac-orleans-tours.fr/maths-2/lycee/arithm/pell.htm>

Contfrac

DÃ©veloppement en fraction continue de n

WIMS wims.unice.fr --- XIAO Gang

<http://wims.unice.fr/wims/wims.cgi?session=BWDE34A7F5.2&+lang=fr&+module=tool%2Fnumber%2Fcontfrac.fr&+cmd=resume>

Continued fraction BCMATH programs

Keith Matthews

Solving the Pell equation x2 - dy2 = Â±1 (NICF-P), (NSCF)

<http://www.numbertheory.org/php/CFRAC.html>

Diophantine Sets over Polynomial Rings and Hilbert's Tenth Problem for Function Fields

Jeroen Demeyer

<http://cage.ugent.be/~jdemeyer/papers/demeyer_phd.pdf>

DOCUMENTS - PAPERS

Michael A. Bennett Publication List

Solving families of simultaneous Pell equations

<http://www.math.uiuc.edu/~mabennet/publ.html>

Pell's equation

<http://www.math.ust.hk/excalibur/Vol_6_no_3.pdf>

Solving the Pell Equation

H W Lenstra Jr.

<http://www.ams.org/notices/200202/fea-lenstra.pdf>

DÃ©veloppement d'un rÃ©el en fractions continues

M. Couchouron PrÃ©paration Ã l'AgrÃ©gation Rennes I

<http://agreg-maths.univ-rennes1.fr/documentation/docs/fraccont.pdf>

J. L. Lagrange Solution d'un ProblÃ¨me d'arithmÃ©tique

<http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=41029>

Archimedes' Cattle Problem (1998)

Ilan Vardi American Mathematical Monthly

this paper is to take the Cattle Problem out of the realm of the \astronomical" and put it into manageable form. This is achieved in formulas (12) and (13) which give explicit forms for the solution.

vardi98archimedes.pdf

<http://citeseer.ist.psu.edu/old/vardi98archimedes.html>

Continued fractions from Euclid to the present day (2000)

Philip

<http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.33.3491>

Les taureaux, l'internet et les quanta: L'arithmetique des tres grands nombres

Henri Darmon May

solution du probleme d'Archimede au debut du 20eme siecle, \une sphere du diametre de la voie lacteee, que la lumiere prend dix mille ans a traverser, ne contiendrait qu'une partie inme de ce troupeau, a 1 supposer m^eme que la taille de chaque animal ne depass^at point celle de la plus minuscule bacterie"...

<http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.15.9202>

On the solvability of the Diophantine equation $dV^2-2eVW-dW^2=1$

Kenneth Hardy and Kenneth S. Williams – Pacific J. Math. Volume 124, Number 1 (1986), 145-158.

<http://www.projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.pjm/1102700685>

The Search For An Exhaustive Solution to Pell's Equation

<http://www.lacim.uqam.ca/~plouffe/OEIS/archive_in_pdf/pellequations.pdf>

Pell's Equation

Dusan Djukic

<http://www.imomath.com/tekstkut/pelleqn_ddj.pdf>

Indian Mathemtics

V. S. Varadarajan – University of California

<http://www.math.ucla.edu/~vsv/gamelin.pdf>

The Minkowski Question Mark, GL ( 2 ,Z) and the Modular Group

Linas Vepstas

<http://linas.org/math/chap-minkowski.pdf>

TUTORIELS - TUTORIALS - TUTORS

Pell Equation Mathworld

<http://mathworld.wolfram.com/PellEquation.html>

Pell's equation

Article by: J J O'Connor and E F Robertson

<http://www-groups.dcs.st-and.ac.uk/history/HistTopics/Pell.html>

Pell's Equation

<http://modular.fas.harvard.edu/edu/Fall2001/124/lectures/lecture20/lecture20/node2.html>

Solutions for Pell's Equation Ask Dr. Math

Math Forum Home

<http://mathforum.org/dr.math/problems/weber.12.11.00.html>

Equation de Fermat-Pell

IREM Strasbourg

<http://irem.u-strasbg.fr/php/articles/12_Stoltz.pdf>

RÃ©solution d'une Ã©quation de Pell-Fermat

megamaths

<http://megamaths.perso.neuf.fr/frag/fragc/s3hari0001.pdf>

HISTORIQUES - HISTORY

John Pell

1 March 1611 in Southwick, Sussex, England - 12 Dec 1685 in London, England

Pell worked on algebra and number theory. He gave a table of factors of all integers up to 100000 in 1668. Pell's equation y2 = ax2 + 1, where a is a non-square integer, was first studied by Brahmagupta and Bhaskara. Its complete theory was worked out by Lagrange, not Pell.

<http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Pell.html>

William Brouncker

It is believed that Euler made an error in naming the equation 'Pell's equation', and that he was intending to acknowledge the outstanding contribution made by Brouncker. It is interesting to think that if Euler had not made this error then Brouncker, instead of being relatively unknown as a mathematician, would be universally known through 'Brouncker's equation'.

<http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Brouncker.html>

PELL John anglais, 1611-1685

Serge MEHL chronomath

<http://www.sciences-en-ligne.com/momo/chronomath/chrono1/Pell.html>

Historical Overview of Pell Equations

Derek Smith

<http://lacim.uqam.ca/~plouffe/OEIS/archive_in_pdf/HistoricalPell.pdf>

Indian Mathematics: Redressing the balance

Ian G Pearce (alternative url)

Pell's equation

<http://www-history.mcs.st-andrews.ac.uk/history/Miscellaneous/Pearce/index.html>

List of Indian mathematicians

Wikipedia The chronology of Indian mathematics spans from the Indus valley civilization and the Vedas to Modern times.

Indian mathematicians have made a number of significant contributions to mathematics including place-value arithmetical notation and the concept of zero.

Narayana Pandit (stub)

<http://en.wikipedia.org/wiki/List_of_Indian_mathematicians>

Narayana Pandit

indian mathematicians blog

<http://indianmathematicians.blogspot.com/2007/12/narayana-pandit.html>

Jean Itard – Revue d'histoire des sciences et de leurs applications

<http://www.persee.fr/web/revues/home/prescript/article/rhs_0048-7996_1954_num_7_4_3465>

RÉFÉRENCES - BIBLIOGRAPHIES

The Pell Equation (1658 – 1943)

<http://www.fen.bilkent.edu.tr/~franz/publ/pell.html>

LIENS - LINKS

autres pages sur les Nombres, les Nombres Premiers, l'Analyse, Diophante, Fermat, Catalan.

<liens_arithm.html>

Pell's links

ScienceOxygen.com Mining of Science Knowledge

<http://www.scienceoxygen.com/math/317.html>

Mathematical Gateways to the WWW

<http://www.math.uga.edu/~ntheory/gateways.html>

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Ãquations de Pell-Fermat - Pell

PAGES WEB

ALGORITHMES

DEMOS

OUTILS - TOOLS

DOCUMENTS - PAPERS

TUTORIELS - TUTORIALS - TUTORS

HISTORIQUES - HISTORY

RÉFÉRENCES - BIBLIOGRAPHIES

LIENS - LINKS

Ãquations de Pell-Fermat - Pell