41. Diophantine Equation - Discussion And Encyclopedia Article. Who Is Diophantine E Diophantine equation. Discussion about Diophantine equation. Ecyclopedia or dictionary article about Diophantine equation. http://www.knowledgerush.com/kr/encyclopedia/Diophantine_equation/

42. Diophantine等式 Translate this page Diophantine . a Diophantine Diophantine http://translate.roseville.ca.us/ma/enwiki/zh_cn/Diophantine_equation

供给动力由WorldLingo Diophantine等式 English Italiano Deutsch Nederlands ... Svenska var addthis_pub="anacolta"; Diophantine等式 a Diophantine等式 只。 Diophantine问题比未知的可变物有少量等式并且介入发现为所有等式正确地运作的整数。 在技术语言，他们定义了 Diophantine Diophantus . Diophantine问题被创始的Diophantus的数学研究现在称“Diophantine分析”。 一个线性Diophantine等式是一个等式在二个总和之间 当单独时等式提出一难题和历史上被考虑了， Diophantine等式的一般理论的公式化(在理论之外 Diophantine等式的例子 Diophantine分析 Diophantine分析在印度 Hilbert的第十个问题 ... 指数Diophantine等式 Diophantine等式的例子 在以下Diophantine等式， x y z 这是一个线性Diophantine等式(参见 部分“线性Diophantine等式” n x y z Pythagorean三倍 n Fermat的前个定理 x y z Pell的等式 约翰Pell Brahmagupta Fermat ... Erdős-Straus臆想 n x y z Diophantine分析 问题在Diophantine分析问了包括： Diophantine分析在印度 ‘对Diophantine等式的缺一不可的解答的s贡献可以被追踪回到 Sulba Sutras 文本BC被写在800和500之间BC。 Baudhayana (大约800 BC)发现二套正面缺一不可的解答对一套同时Diophantine等式，并且试图同时Diophantine等式以四个未知数。 Apastamba (大约600 BC)试图同时Diophantine等式以五个未知数。 数学家更晚广泛地学习的Diophantine等式在中世纪印度，是系统地调查方法的一个为Diophantine等式的缺一不可的解答的决心。 系统的方法为发现Diophantine等式的整数解答在印第安文本能被发现从时

43. 디오판투스 방정식 - 수학이 알고싶은 중고대딩들을 위한 수 Translate this page 2010 5 18 http//en.wikipedia.org/wiki/diophantine_equation http//mathworld.wolfram.com/DiophantineEquation.html http://pythagoras0.springnote.com/pages/4438993

44. Reference For Diophantine Equation - Search.com In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. Diophantine problems have http://www.search.com/reference/Diophantine_equation

45. ���Ҽ�ѵ��2009���ļ�ŷ������㷨��Ӧ��_�ٶ��Ŀ� Translate this page 2009 11 13 5 6 http//en.wikipedia.org/wiki/Extended_Euclidean_algorithm http//en. wikipedia.org/wiki/diophantine_equation 7 , http://wenku.baidu.com/view/d9dff705cc17552707220825.html

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46. Full Text Of Quot Diophantus Of Alexandria A Study In The History Of | Facebook Translate this page TripAtlas.com - About diophantine_equation mathematician of the 3rd century, Diophantus of Alexandria, who made a study of and have http://tutorialfacebook.info/search/full text of quot diophantus of alexandria a

Home About Kontak Sitemap Facebook Tutorial and News get new update about facebook featured Games info facebook share ... video full text of quot diophantus of alexandria a study in the history of Loading... Full text of "Diophantus Of Alexandria A Study In The History Of ... Full text of "Diophantus Of Alexandria A Study In The History Of Greek Algebra" Full text of "Diophantus of Alexandria; a study in the history of ... Full text of "Diophantus of Alexandria; a study in the history of Greek algebra" Diophantus of Alexandria Diophantus of Alexandria Diophantus: Facts, Discussion Forum, and Encyclopedia Article Diophantus: Biography from Answers.com ... Diophantus II.VIII - Wikipedia, the free encyclopedia Diophantus II.IX reaches the same solution by an even quicker ... Edit this page; History ... Text is available under the Creative Commons Attribution ... ... the lives and studies of Pierre de Fermat and Diophantus of Alexandria ... knowledge of Diophantus rests upon the fact that he quotes ... st-and.ac.uk/~history/Mathematicians/Diophantus ... Pappus of Alexandria: Facts, Discussion Forum, and Encyclopedia ...

47. LINEAR DIOPHANTINE EQUATIONS A web tool for solving Diophantine equations of the form ax + by = c. http://www.thoralf.uwaterloo.ca/htdocs/linear.html

Solving ax +by = c a b c

48. Diophantine Equation -- From Wolfram MathWorld A Diophantine equation is an equation in which only integer solutions are allowed. Hilbert's 10th problem asked if an algorithm existed for determining whether an arbitrary http://mathworld.wolfram.com/DiophantineEquation.html

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Interactive Demonstrations Diophantine Equation A Diophantine equation is an equation in which only integer solutions are allowed. Hilbert's 10th problem asked if an algorithm existed for determining whether an arbitrary Diophantine equation has a solution. Such an algorithm does exist for the solution of first-order Diophantine equations. However, the impossibility of obtaining a general solution was proven by Yuri Matiyasevich in 1970 (Matiyasevich 1970, Davis 1973, Davis and Hersh 1973, Davis 1982, Matiyasevich 1993) by showing that the relation (where is the th Fibonacci number ) is Diophantine. More specifically, Matiyasevich showed that there is a polynomial in , and a number of other variables , ... having the property that iff there exist integers , ... such that Matiyasevich's result filled a crucial gap in previous work by Martin Davis, Hilary Putnam, and Julia Robinson. Subsequent work by Matiyasevich and Robinson proved that even for equations in thirteen variables, no algorithm can exist to determine whether there is a solution. Matiyasevich then improved this result to equations in only nine variables (Jones and Matiyasevich 1982). Ogilvy and Anderson (1988) give a number of Diophantine equations with known and unknown solutions.

49. Linear Diophantine Equations Linear Diophantine Equations. A Diophantine equation is an equation which is to be solved over the integers. A linear Diophantine equation of the form has solutions if and only if. http://marauder.millersville.edu/~bikenaga/numbertheory/linear-diophantine/linea

Linear Diophantine Equations A Diophantine equation is an equation which is to be solved over the integers. A linear Diophantine equation of the form has solutions if and only if . There is a similar result for linear Diophantine equations in more than 2 variables. A Diophantine problem is one in which the solutions are required to be integers. Abusing terminology, I'll refer to Diophantine equations , meaning equations which are to be solved over the integers. Example. has many solutions over the reals; for example, However, this equation has no nonzero integer solutions. Example. Since , there are integers x and y such that For example, , and . That is, the Diophantine equation has solutions - in fact, infinitely many solutions. Theorem. Let . Consider the Diophantine equation (a) If , there are no solutions. (b) If , there are infinitely many solutions of the form Here is a particular solution, and Before I give the proof, I'll give some examples, and also discuss the three variable equation Example.

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

The Collection of Computer Science Bibliographies Collection Home Up: Bibliographies on Mathematics Bibliography on Hilbert's Tenth Problem About Browse Statistics Number of references: Last update: December 10, 1999 Number of online publications: Supported: 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 page 200 results per page sort by score year online papers only You may use Lucene syntax , available fields are: ti (title), au (author), yr (publications year). Information on the Bibliography Authors: Maxim Vsemirnov (email mangled to prevent spamming) Yuri Matiyasevich Laboratory of Mathematical Logic St. Petersburg Division of Steklov Institute of Mathematics (POMI) Russian Academy of Sciences Abstract: The ultimate goal of this bibliography would be to contain references to all publications connected with the undecidability of Hilbert's Tenth Problem. Keywords: Hilbert's Tenth Problem, Diophantine equations, computable functions

51. Diophantine Equation: Definition From Answers.com n. An algebraic equation with two or more variables whose coefficients are integers, studied to determine all integral solutions. After Diophantus , thirdcentury A.D. Greek http://www.answers.com/topic/diophantine-equation

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

Egyptian Fractions Nowadays, we usually write non-integer numbers either as fractions (2/7) or decimals (0.285714). The floating point representation used in computers is another representation very similar to decimals. But the ancient Egyptians (as far as we can tell from the documents now surviving) used a number system based on unit fractions : fractions with one in the numerator. This idea let them represent numbers like 1/7 easily enough; other numbers such as 2/7 were represented as sums of unit fractions (e.g. 2/7 = 1/4 +1/28). Further, the same fraction could not be used twice (so 2/7 = 1/7 + 1/7 is not allowed). We call a formula representing a sum of distinct unit fractions an Egyptian fraction This notation is cumbersome and difficult to compute with, so the Egyptian scribes made large tables so they could look up the answers to arithmetic problems. However there is also some interesting mathematics associated with the problem of converting modern fraction notation into the Egyptian form. A number of famous mathematicians have looked at this problem, and invented different ways of doing this conversion process. Each of these methods has advantages and disadvantages in terms of the complexity of the Egyptian fraction representations it produces and in terms of the amount of time the conversion process takes. There are still some unsolved problems about whether some of these processes finish, or whether they get into an infinite loop. To investigate some of these questions, I wrote a

53. PlanetMath: Diophantine Equation A Diophantine equation is an equation between polynomials in finitely many variables over the integers. Usually one is interested in integral solutions. http://planetmath.org/encyclopedia/DiophantineEquation.html

(more info) Math for the people, by the people. donor list find out how Encyclopedia Requests ... Advanced search Login create new user name: pass: forget your password? Main Menu sections Encyclopædia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About Diophantine equation (Definition) A Diophantine equation is an equation between polynomials in finitely many variables over the integers . Usually one is interested in integral solutions Generally, solving a Diophantine equation is not as straightforward as solving a similar equation in the real numbers . For example, consider this equation: $$x^4+ y^4 = z^4$$ It is easy to find real numbers $x, y, z$ that satisfy this equation: pick any arbitrary $x$ and $y$ , and you can compute a $z$ from them. But if we require that $x, y, z$ all be integers, it is no longer obvious at all how to find solutions. Even though raising an integer to an integer power yields another integer, the reverse is not true in general. As it turns out, of course, there are no solutions to the above Diophantine equation: it is a case of

54. Diophantine Equation - Definition Diophantine equation definition from the mondofacto online medical dictionary http://www.mondofacto.com/facts/dictionary?Diophantine equation

55. Swett, Research, Erdos-Strauss Conj The page establishes that the conjecture is true for all integers. Tables and software by Allan Swett. http://math.uindy.edu/swett/esc.htm

Allan Swett, Current Research on ESC... rev. 10/28/99 The Erdos-Strauss Conjecture 4/n = 1/a + 1/b + 1/c, (Note: 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 ESC(n) is true for n = 2, 5, 8, 11, 14, 17, ... (simply take x = 0, 1, 2, 3, 4, 5, ...). That is, ESC(n) is true for all positive integers n which are congruent to 2, mod 3. (Two integers are said to be "congruent mod n", if and only if n divides their difference. We abbreviate the fact that A and B are congruent mod n as A == B (mod n) .) A "generic" identity provides a set of similar results: Vocabulary: S(n) AX + W == (mod 4n-1) for some positive integer divisors X and W of n. Let E(n) denote the set of positive integers congruent, mod 4n-1, to an element of S(n). Then Theorem: Link to a proof of the Theorem.

56. Diophantine Equation | Define Diophantine Equation At Dictionary.com –noun Mathematics . an equation involving more than one variable in which the coefficients of the variables are integers and for which integral solutions are sought. Use http://dictionary.reference.com/browse/Diophantine equation

57. Diophantine Equation In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. Diophantine problems have fewer equations than unknown http://english.turkcebilgi.com/Diophantine equation

EnglishInfo Search Türkçe Home Information Translation ... diophantine equation Information about diophantine equation diophantine equation Information about diophantine equation Double click any English word, to find Turkish meaning In mathematics , a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations. In more technical language, they define an algebraic curve algebraic surface or more general object, and ask about the lattice points on it. The word Diophantine refers to the Hellenistic mathematician of the 3rd century, Diophantus of Alexandria , who made a study of such equations and was one of the first mathematicians to introduce symbolism into algebra . The mathematical study of Diophantine problems Diophantus initiated is now called "Diophantine analysis". A linear Diophantine equation is an equation between two sums of monomials of degree zero or one.

58. Clemens Heuberger - 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

Clemens Heuberger - Thue equations Diophantine equations Since antiquity, many people try to solve equations over the integers, 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. Among his 23 Problems, Hilbert raised the question, whether there exists an algorithm to solve any given polynomial diophantine equation; the negative answer has been given by Matijasevic in 1970. So the research interest in diophantine equations is to find classes of such equations which can be solved. Thue equations In 1909, A. Thue considered a special family of equations F(X,Y) = m, where F is an irreducible homogeneous form of degree n at least 3 and m is a nonzero integer. This type of equations is called after him since then; he proved that such an equation only has a finite number of solutions. His proof, however, is not constructive, so it does not lead to an algorithm. Only with Baker's lower bounds for linear forms in logarithms of algebraic numbers (19661968), effective bounds for the solution of many diophantine equations can be given. Since that time, many bounds have been improved and algorithms have been developed to solve one single Thue-equation in reasonable time on a computer (see Bilu and Hanrot). Parametrized Thue equations In 1990, E. Thomas studied a parametrized family of cubic Thue equations: It turns out that there exist only a few "trivial" solutions for large values of the parameter.

59. Math Forum - Ask Dr. Math Archives: Diophantine Equations If a and b are relatively prime positive integers, prove that the Diophantine equation axby = c has infinitely many solutions in the positive integers. http://mathforum.org/library/drmath/sets/select/dm_diophantine.html

Ask Dr. Math Diophantine Equations Dr. Math Home Elementary Middle School High School ... Dr. Math FAQ Diophantine Equations , a selection of answers from the Dr. Math archives. Diophantine Equations We have searched the Web for information about Diophantine equations. Diophantine Equations, Step by Step Find all positive integer solutions to 43x + 7y + 17z = 400. Integer Solutions of ax + by = c Given the equation 5y - 3x = 1, how can I find solution points where x and y are both integers? Also, how can I show that there will always be integer points (x,y) in ax + by = c if a, b and c are all integers? Buying Cows, Pigs, and Chickens A farmer buys 100 animals for $100. The animals include at least one cow, one pig, and one chicken. If a cow costs $10, a pig costs $3, and a chicken costs $0.50, how many of each did he buy? How Many Mice, Cats, and Dogs? You must spend $100 to buy 100 pets, choosing at least one of each pet. The pets and their prices are: mice @ $0.25 each, cats @ $1.00 each, and dogs @ $15.00 each. How many mice, cats, and dogs must you buy? Money Puzzle A man goes to the bank and asks for x dollars and y cents.

60. SOLVE A DIOPHANTINE EQUATION In the fields below, enter the INTEGER coefficients of x and y and the constant term. Then click on the solve it button. Equation x + y = http://www.math.csusb.edu/notes/maple/plot/dioph.html

Previous: Tools page Up: Contents page SOLVE A DIOPHANTINE EQUATION In the fields below, enter the INTEGER coefficients of x and y and the constant term. Then click on the solve it button. Peter Williams Sat Oct 26 23:31:28 PDT 1996

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