NOVA Online presents The Proof, including an interview with Andrew Wiles, an essay on Sophie Germain, and the Pythagorean theorem.

Fermat's last theorem Number theory index History Topics Index Pierre de Fermat died in 1665. Today we think of Fermat as a number theorist, in fact as perhaps the most famous number theorist who ever lived. It is therefore surprising to find that Fermat was in fact a lawyer and only an amateur mathematician. Also surprising is the fact that he published only one mathematical paper in his life, ...

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 ...

Computing minimal sums of like powers for extended Euler conjecture ...

Information about various types of diophantine equations.

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 ...

Detailed information about Fermat's Last Theorem.

Diophantine m-tuples, sets with the property that the product of any two of its distinct elements is one less than a square ...

Description of the Beal Conjecture and the Beal Prize.

Solves quadratic Diophantine equations (integer equations of the form a x^2 + b xy + c y^2 + dx + ey + f = 0) ...

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 ...

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 ...

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, ...

Bibliography on Hilbert's Tenth Problem. This bibliography is a part of the Computer Science Bibliography Collection.

Properties and Calculation of pythagorean Triples ...

Detailed information about Euler's Sum of Powers Conjecture.

B= ( a - m ) / 2 / m ___ c = b + m___ Pythagoras-Tripel-Programm von Heinz Becker nur der Wert a wird abgefragt. Urheberrecht: Heinz Becker ...

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, ...

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 ...

Power Page Interesting stuff about powers of numbers Index About Notation Pythagorean Triplets Almost-Isoceles Triples Almost 30-60 Triples Chains of Consecutive Squares Pythagorean Quartets Fermat's Last Theorem Euler's Conjecture Sums of Cubes (Cubic Quartets) Sums of Fourth Powers Sums of Fifth and Higher Powers Sums of Powers of Consecutive Integers Multigrades About Notation To save writing ...

Beal's Conjecture: A Search for Counterexamples Beal's Conjecture is this: There are no positive integers x, m, y, n, z, r satisfying the equation xm + yn = zr where m, n, r 2 and x, y, z are co-prime (that is, gcd(x, y) = gcd(y, z) = gcd(x, z) = 1). There is a $75, 000 prize for the first proof or disproof of the conjecture. The conjecture is obviously related to Fermat's Last Theorem, which was proved ...

Equal Sums of Like Powers - my dissertation This dissertation (written for the MMath degree at Oxford) looks at various problems of the form 'in how many ways can an integer be written as a sum of a given number of positive nth powers'. About the only proven result in this field is that there exist integers writable in arbitrarily many ways as a sum of two positive cubes; I give this result with ...

PROOF OF FERMAT'S LAST THEOREM James Constant ConstantRCS@cs.com Fermat's Last Theorem is solved using the binomial expansion. Introduction ........Fermat (1601-1665) claimed in 1637 to have discovered a marvelous proof of his last theorem.1 (1) The Binomial Expansion ........Before seeking the solution to Fermat's last theorem, consider the binomial expansion2 (2) in which a is an arbitrary ...

Around Goedel's Theorem. Textbook for students. Section 4. By K.Podnieks ...

Brief overview of Fermat's Last Theorem.