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Diophantine Equations
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Searchable, ~400 items.
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Bibliography on Hilbert's Tenth Problem Number of online publications:5Supported:yes Most recent reference:February 1993 Query: in any author title field; Publication year: in since before four digit years) Options: Results as Citation Results in BibTeX 10 results per page 40 results per page 100 results per...Dave Rusin's guide to Diophantine equations.
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11D: Diophantine equations Applications and related fields See also 11GXX, 14GXX. In particular, discussion of many examples and families of equations has been moved to pages for (arithmetic) algebraic geometry; the dividing line is unclear sorry. Diophantine equations whose solution set is one-dimensional...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.
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Swett, Research, Erdos-Strauss Conj Some of the linked pages are under revision Principal Ideas, Part 1: A C Program One may establish ESC(n) for a particular class of integers n using an identity. For example, the identity 4/(2+3x 1/(2+3x 1/(1+x 1 1+x)(2+3x establishes that...Definition of the problem and a list of special cases that have been solved, by Clemens Heuberger.
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Clemens Heuberger Thue equations Pythagoras for instance described all integers being the sides of a rectangular triangle. After Diophantus von Alexandrien such equations are called diophantine equations. Since that time, many mathematicians worked on this topic, such as Fermat, Euler, Kummer, Siegel, and Wiles....Statement of the problem in several languages, history of the problem, bibliography and links to related WWW sites.
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Hilbert Tenth Problem: database index The aim of this page is to promote research connected with the negative solution of Hilbert's Tenth Problem. The negative solution of this problem and the developed techniques have a lot of applications in theory of algorithms, algebra, number theory,...A survey by José Felipe Voloch.
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Diophantine geometry in characteristic p: a survey Diophantine geometry in characteristic p: a survey José Felipe Voloch it goes without saying that the function-fields over finite fields must be granted a fully simultaneous treatment with number-fields, instead of the segregated status, and at best the separate but...A Javascript calculator for pythagorean triplets.
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pythagorean triplets pythagorean triples T consists of three natural numbers x, y and z with x2 y2 z2. PT's with greatest common divisor 1 TPT's are of particular interest. Theorem 1 Every PT can be obtained in a unique way as a product of...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.
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Hilbert's Tenth Problem. Diophantine Equations. By K.Podnieks Adjust your browser window Right 4. Hilbert's Tenth Problem Statement of the problem: 10. Determining the solvability of a Diophantine equation. Given a Diophantine equation with any number of unknowns and with rational integer coefficients: devise a process, which could...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.
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Dario Alpern's Generic Two integer variable equation solver If you are using that software, you should enable JavaScript, and then reload this page....A JavaScript applet which reads a and gives integer solutions of a^2+b^2 = c^2.
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Pythagorean Triples b=(a²/m m)/2 c=b+m Pythagorean Triplets Web Counter...Sets with the property that the product of any two distinct elements is one less than a square. Notes and bibliography by Andrej Dujella.
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Diophantine m-tuples The problem of the construction of Diophantine m-tuples, i.e. sets with the property that product of any two of its distinct elements is one less then a square, has a very long history. There are some new results in this...Triangles in the Euclidean plane such that all three sides are rational. With tables of Heronian and Pythagorean triples.
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Rational Triangles Triangle as a triangle in the Euclidean plane such that all three sides measured relative to each other are rational. Once, it was thought that all triangles were rational. The discovery of counterexamples is attributed to the Pythagoreans. Any triangle...John Robertson's treatise on how to solve Diophantine equations of the form x^2 - dy^2 = N.
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Solving General Pell Equations An improved version of what used to be here is now a PDF file at my homepage. Look for the PDF file titled Solving the generalized Pell equation The old HTML page (uncorrected, un-enhanced, on some browsers some math symbols...Record solutions.
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Pell's equation Large fundamental solutions of Pell's equation Introduction Results References Links Contact [Up] Introduction LetA be a positive integer which is not a perfect square. It is well known that there exist an infinite number of integer solutions of the equation...Notes by Jamie Bailey and Brian Oberg. Illustrates the method on FLT with exponent 4.
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Fermat's Method of Infinite Descent Fermat received his degree in Civil Law at the University of Orleans before 1631 and served as a lawyer and then a councillor at Toulouse. The political and legal path Fermat chose is attributed to the trends of upward social...On-line Pell Equation solver by Michael Zuker.
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Diophantus Quadraticus: X^2 dY^2 1 Enter a positive integer value for d. d must not be a perfect square. Verbose mode: Off: On: Professor Michael Zuker Department of Mathematical Sciences Rensselaer Polytechnic Institute zukerm@rpi.edu...Some of conjectures and open problems, compiled at AIM.
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Rational and integral points on higher dimensional varieties This web page highlights some of the conjectures and open problems concerning Rational and integral points on higher dimensional varieties. If you would like to print a hard copy of the whole...MAGMA code to solve Diophantine equations of the form F(x)=G(y), for which Runge's condition is satisfied. Created by Szabolcs Tengely.
http://www.math.leidenuniv.nl/~tengely/main2.html
Articles, computations and software in Magma and GP by Martin Bright.
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Diagonal quartic surfaces Diagonal quartic surfaces This is Martin Bright's page about diagonal quartic surfaces. This page contains various bits and pieces which you can download. It is not really prepared for general use, and certainly not documented; but there is a small...A web tool for solving Diophantine equations of the form ax + by = c.
http://www.thoralf.uwaterloo.ca/htdocs/linear.html
A web text by Fred Barnes on 60-, 90-, and 120-degree integer-sided triangles.
http://www.geocities.com/fredlb37/