 Entropia.com
The Global Internet Community for Science and Mathematics Distributed Research Computing, Entropia.com is a community dedicated to performing real research on a massive scale using ordinary home and office computers connected through the Internet. Entropia.org's
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 Equal Sums of Like Powers  Chen Shuwen
An extensive collection of equal sums of like powers, especially those that are solutions to multigrade equations.
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 Equal Sums of Like Powers  Chen Shuwen, People's Republic of China
On the integer solutions of the Diophantine system.
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 Equipalindromic Numbers  Len Smiley
A description of the expansion of square root of natural numbers into continued fractions, and the strings of palindromes that can emerge from them. With a table of the first 100 natural numbers and their equipalindromic quadratic polynomials.
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 The ErdosStrauss Conjecture (ESC)  Allan Swett
The conjecture states that 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. With links to
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 The Euclidean Algorithm  David Sumner
Find the greatest common divisor (GCD) online using the Euclidean Algorithm. Enter two numbers, and the JavaScript calculates GCD, least common multiple (LCM), and linear combination; and displays the steps of the algorithm.
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 Euclid's Algorithm  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
An explanation of Euclid's algorithm for finding the greatest common divisor (gcd) of any pair of numbers, and a relation to the fundamental theorem of arithmetic, with links to related pages on Euclid's Game, binary Euclid's Algorithm, more on the gcd
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 Euler and Erdös
Blog of selfdescribed amateur research in tribute to Leonhard Euler and Paul Erdös, "muses" to an author who considers it "hard to find math blogs aimed at undergraduates." Posts, which date back to May, 2013, have included "Envelopes and Astroids,"
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 Euler Bricks and Perfect Polyhedra  Ivars Peterson (MathTrek)
"In the October Mathematics Magazine, Blake E. Peterson of Brigham Young University in Provo, Utah, and James H. Jordan of Washington State University in Pullman draw attention to perfect boxes and polyhedra. Their starting point is the problem of finding
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 Euler Function and Theorem  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A description with proof, lemma, and related links.
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 Everything Is Mathematical  RBA Contenidos Editoriales y Audiovisuales S.A.
Based on the series of books, published weekly in association with The Times and presented by Marcus du Sautoy, which aims to demonstrate clearly how mathematics shapes the world around us. Blog posts, which date back to September, 2012, have included
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 Examination Papers  University of Cambridge
Download PDF and PostScript files of Cambridge's mathematical tripos examination papers from the past decade. See also the exam papers from Natural Sciences Tripos (NST) and Part III (postgraduate).
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 Expositions and Notes  Ben Green; Trinity College, Cambridge, UK
DVI files on topics in sieve theory and combinatorial number theory.
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 Factorization using the Elliptic Curve Method  Dario Alejandro Alpern
A Java applet that factors numbers up to 1000 digits long, outputting their number of divisors, sum of divisors, Euler's totient, Moebius number, and sum of squares. Also accepts numerical expressions.
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 The Famous Wonders of the Mind / Les Merveilles de l'Esprit  Nan Zhu, Yifei Zhu  ThinkQuest '99
Math and science stories teach students some famous tricks and formulae through history, games, and short essays on the golden section, the Fibonacci sequence, Pascal's triangle, logarithms, the Bridges of Konisberg, the binary system, etc. In English
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 Fermat and His Method of Infinite Descent  Jamie Bailey, Brian Oberg
The basic method of the infinite descent is as follows: Assume one wants to prove no solution exists with a certain property. First, assume a positive integer, x, posseses such a property. Next, deduce that there exists some positive integer y < x
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 Fermat Project Description  Hanson, Kaplan, Heng; Center for Innovative Computer Applications (CICA)
Images, movies, videos, publications, presentations. An animation presents a popularized introduction to Fermat's Last Theorem. Threedimensional mathematical depictions are used in the beginning of the film to illustrate the meaning of the mathematical
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 Fermat's Last Theorem  BBC Online  Horizon
About Andrew Wiles and the solving of FLT  with a link to a long programme transcript.
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 Fermat's Last Theorem  David Shay
Site contents: The birth of the problem; Proofs for special cases; First steps in general proofs; The computer enters the picture; Is there a proof at all?; There are bigger problems; There are failures too; TaniyamaShimura conjecture; Here is the proof!;
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 Fermat's Last Theorem (FLT)  Math Forum, Ask Dr. Math FAQ
What is the current status of Fermat's Last Theorem?
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 Fermat's Last Theorem Poetry Challenge  Jeremy Teitelbaum
The proof of Fermat's last theorem by Andrew Wiles and Richard Taylor was presented to an audience of over 300 people during a tenday conference at Boston University in August, 1995. At that conference, Jeremy Teitelbaum issued a poetry challenge asking
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 Fermat's Last Theorem  Richard Pinch
Order a video that gives a brief history of the attempts that have been made to solve Fermat's theorem (said to have been his last), and outlines some of the problems that have been encountered along the way.
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 Fermat's Little Theorem  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A description with proof involving modular arithmetic, and related links.
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 Fermat's room  Javier Martín
Solve puzzles playing this Java math adventure game, also available in Spanish. Based on a film by the same name.
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 Fibonacci at Random  Ivars Peterson  Science News Online
In a book completed in 1202, mathematician Leonardo of Pisa (also known as Fibonacci) posed the following problem: How many pairs of rabbits will be produced in a year, beginning with a single pair, if every month each pair bears a new pair that becomes
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 The Fibonacci Series  Matt Anderson, Jeffrey Frazier, and Kris Popendorf; ThinkQuest 1999
The Fibonacci Series is deceptively simple, but its ramifications and applications are many. Learn more about the Fibonacci Series itself: an introduction, the rabbit problem, Binet's formula, the successor formula (given only one term in the Fibonacci
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 The Fifth Taxicab Number is 48988659276962496  David W. Wilson
An article on the 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. The nth taxicab number is the least number which can be expressed as a sum of two positive cubes in n distinct
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 FillItIn Outline Mathematics  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A collection of outline solutions to various problems: word and logic problems, problems from arithmetic, number theory and geometry. Solutions are practically complete with a few essential pieces omitted and to be filled in by the student.
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 First occurrences of squarefree gaps and an algorithm for their computation
 Louis Marmet
This page reports the results of a search for first occurrences of squarefree gaps using an algorithm based on the sieve of Eratosthenes. The source code is supplied.
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 Fractions and Infinite Series  Don Cohen (The Mathman)
Young children (ages 67) learn to add fractions through graphing and partial sums, and about infinite series. A sample problem with answers from Chapter 1 of Don Cohen's worksheet book.
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 Fragments of the Past  Ivars Peterson (MathLand)
Historians of mathematics now generally agree that scholars in China, India, and the Islamic world produced remarkably sophisticated mathematics between the fifth and the fifteenth centuries. However, most would probably still argue that Europeans in
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 Freakonometrics  Arthur Charpentier
Blog by a Montreal professor of actuarial science "addicted to R." Posts, which date back to March, 2007, have included "Dynamic dependence ordering for Archimedean copulas and distorted copulas," "Pricing catastrophe options in incomplete markets," "Estimation
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 Free Online Books  PSPXWorld.com
Free books for download or viewing online, in computer science and mathematics.
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 From Lewis Carroll to Archimedes  Cut the Knot!, Alexander Bogomolny
On March 29, 1879, Vanity Fair began offering its subscribers a new weekly puzzle invented by Lewis Carroll... on March 17, 1953 Frank Gray, a research scientist at Bell Labs, filed patent no. 2632058, for the Gray code encoding
the vacuum tube. An ndigit
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 Front for the Mathematics ArXiv  Univ. of California, Davis
U.C. Davis front end for the xxx.lanl.gov ePrint archive, a major site for mathematics preprints that has incorporated many formerly independent specialist archives including alggeom, functan, dgga, qalg, autofms, cdhg, MAGNUS, Several Complex
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 Fun With Num3ers
A blog of mathematical puzzles, mostly in number theory. Posts, which date back to January, 2012, have included "Using digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 only once (Part Two)," "Pythagorean triple – Digits Reversed," "Concatenation puzzle: when (A 
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 Gallica  Bibliothèque nationale de France
Une sélection de documents numérisés qui montrent la diversité des collections manuscrites de la Bibliothèque nationale de France: les oeuvres de Joseph Liouville, Augustin Cauchy, Joseph Fourier, Henri Poincaré, Janos
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 GANG Knot Library  Dept. of Mathematics & Statistics, Univ. of Massachusetts, Amherst
A library of Energy Minimizing Knots and Links. Select a knotimage or category to see more members of the knot's family. The catalog contains knots up to 8 crossings. 2,q torus knots and links; Rational link with two, three, and fourterm continued
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 Gaussian Integer Calculator  Dario Alejandro Alpern
Applet that evaluates numerical expressions using Gaussian integers, factors Gaussian integers, and evaluates functions, including the greatest common divisor (GCD), modular inversion, and modular exponentiation, among others.
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 GEM: Gateway to Educational Materials  National Library of Education (NLE)
A database for education links, intended to be more useful for teachers than a search engine. It records the resources of its consortium members (information on joining the consortium is available onsite). Users are able to: browse through lists organized
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 General Mathematics, NZ (Funk & Wagnalls Multimedia Encyclopedia)  Lycos Zone: Mathematics
Short articles on basic mathematics, including biographical information about mathematicians, from John Napier to Zeno of Elea.
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 Generic Two integer variable equation solver  Dario Alpern
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 stepbystep (or teach) mode. With a link to his description of the solving methods.
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 G. J. Chaitin
Currently a member of the computer systems and software department at the IBM Watson Research Center in New York, Chaitin created algorithmic information theory, which combines, among other elements, Shannon's information theory and Turing's theory of
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 G J Chaitin Home Page  Greg Chaitin
From the author of Algorithmic Information Theory, Information, Randomness & Incompleteness, InformationTheoretic Incompleteness, The Limits of Mathematics, The Unknowable, Exploring Randomness, Conversations with a Mathematician, From Philosophy
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 Goldbach's Prime Pairs  Ivars Peterson (MathTrek)
Prime numbers serve as building blocks in the mathematics of whole numbers. Evenly divisible only by themselves and one, primes are a rich source of speculative ideas that mathematicians often find simple to state but difficult to prove. The Goldbach
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 The Golden Section Ratio: Phi  Ron Knott
Contents: What is the Golden Ratio (or Phi)?  A simple definition of Phi, A bit of history; Phi to 2000 decimal places; Phi and the Fibonacci numbers  Another definition of Phi, A formula for Phi using a continued fraction, Rational Approximations
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 Got Math?  Dave Radcliffe
Blog by a community college math instructor and selfdescribed "GeoGebra fanatic." Posts, which date back to December, 2010, have included "Stacking cannonballs," "Counting with Integrals," "A Paradoxical Dissection," "Gelfand's Question," "Imagining
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 Greek Mathematics and its Modern Heirs  SunSITE's Vatican Exhibit; Library of Congress
Classical roots of the scientific revolution. An essay on the history of Greek Math, with sample math problems. Covers Euclid's Elements and Optics, Archimedes' Works, Piero della Francesca's De quinque corporibus regularibus, and links to Ptolemy's Geography
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 Grothendieck Circle  Leila Schneps et al.
Alexandre Grothendieck's published articles, unpublished research, letters, and translations: The Cohomology Theory of Abstract Algebraic Varieties, Standard Conjectures on Algebraic Cycles, Hodge's General Conjecture Is False for Trivial Reasons, Groupes
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 HAKMEM  Beeler, Gosper, Schroeppel; Artificial Intelligence Laboratory, MIT
A list of math and computerrelated problems, unsolved in 1972 when the list originated, compiled "with the hope that a record of the random things people do around here can save some duplication of effort  except for fun." Topics include: Geometry,
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