Egyptian Fractions
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 ...
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Diophantine Equations
Information about various types of diophantine equations.
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Hilbert Tenth Problem: database index
Welcome to Hilbert's Tenth Problem page! Choose the nearest mirror site: St.Petersburg (Russia) - master; Greenville (USA) 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, model theory, proof ...
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Diophantine m-tuples
Diophantine m-tuples, sets with the property that the product of any two of its distinct elements is one less than a square ...
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Diophantine geometry in characteristic p: a survey
Next: Introduction Diophantine geometry in characteristic p: a survey Jos 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 equal facilities, which hitherto have been their lot. That, far from losing by such treatment, both races ...
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Swett, Research, Erdos-Strauss Conj
Allan Swett, Current Research on ESC... rev. 10/28/99 The Erdos-Strauss Conjecture The Erdos-Strauss conjecture (ESC) is the statement 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. * Let ESC(n) abbreviate the statement that * is true for a particular positive integer n. ESC(n) is known to be true for all integers n, 1 n = 10^8. This ...
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Clemens Heuberger - Thue equations
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, ...
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Pell's equation
Record-Holder Solutions of Pell's Equation Introduction Results References Links Contact Introduction Let A 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 Ax^2+1=y^2, known as Pell's equation. (Because the current generation of browsers display subscripts and superscripts in a very unsatisfactory way, ...
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Rational Triangles
Rational Triangles Definition Define a Rational 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 similar to a rational triangle is rational also. Take as a unit the greatest common measure of ...
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Equal Sums of Like Powers