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Beal conjecture, the Glossary

The Beal conjecture is the following conjecture in number theory: Equivalently, The conjecture was formulated in 1993 by Andrew Beal, a banker and amateur mathematician, while investigating generalizations of Fermat's Last Theorem.^[1]

39 relations: Abc conjecture, American Mathematical Society, Andrew Beal, Andrew Wiles, Édouard Lucas, Berkeley Open Infrastructure for Network Computing, Bjorn Poonen, Catalan's conjecture, Conjecture, Coprime integers, Counterexample, Distributed computing, Euler's sum of powers conjecture, Faltings's theorem, Fermat's Last Theorem, Fermat–Catalan conjecture, Gaussian integer, Generalization, Google, Henri Darmon, Integer, Jacobi–Madden equation, Jordan Ellenberg, List of amateur mathematicians, Loïc Merel, Notices of the American Mathematical Society, Number theory, Peter Norvig, Pierre de Fermat, Preda Mihăilescu, Prime number, Prouhet–Tarry–Escott problem, Pythagorean quadruple, Pythagorean Triangles, Pythagorean triple, Special case, Sums of powers, Taxicab number, Wacław Sierpiński.
Abc conjecture

Abc conjecture

The abc conjecture (also known as the Oesterlé–Masser conjecture) is a conjecture in number theory that arose out of a discussion of Joseph Oesterlé and David Masser in 1985. Beal conjecture and abc conjecture are conjectures and Unsolved problems in number theory.

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American Mathematical Society

The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.

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Andrew Beal

Daniel Andrew Beal (born November 29, 1952) is an American banker, businessman, investor, and amateur mathematician.

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Andrew Wiles

Sir Andrew John Wiles (born 11 April 1953) is an English mathematician and a Royal Society Research Professor at the University of Oxford, specialising in number theory.

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Édouard Lucas

François Édouard Anatole Lucas (4 April 1842 – 3 October 1891) was a French mathematician.

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Berkeley Open Infrastructure for Network Computing

The Berkeley Open Infrastructure for Network Computing (BOINC, pronounced – rhymes with "oink") is an open-source middleware system for volunteer computing (a type of distributed computing).

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Bjorn Poonen

Bjorn Mikhail Poonen (born July 27, 1968, in Boston, Massachusetts) is a mathematician, four-time Putnam Competition winner, and a Distinguished Professor in Science in the Department of Mathematics at the Massachusetts Institute of Technology.

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Catalan's conjecture

Catalan's conjecture (or Mihăilescu's theorem) is a theorem in number theory that was conjectured by the mathematician Eugène Charles Catalan in 1844 and proven in 2002 by Preda Mihăilescu at Paderborn University. Beal conjecture and Catalan's conjecture are abc conjecture, conjectures and Diophantine equations.

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Conjecture

In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Beal conjecture and conjecture are conjectures.

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Coprime integers

In number theory, two integers and are coprime, relatively prime or mutually prime if the only positive integer that is a divisor of both of them is 1.

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Counterexample

A counterexample is any exception to a generalization.

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Distributed computing

Distributed computing is a field of computer science that studies distributed systems, defined as computer systems whose inter-communicating components are located on different networked computers.

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Euler's sum of powers conjecture

In number theory, Euler's conjecture is a disproved conjecture related to Fermat's Last Theorem. Beal conjecture and Euler's sum of powers conjecture are Diophantine equations.

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Faltings's theorem

Faltings's theorem is a result in arithmetic geometry, according to which a curve of genus greater than 1 over the field \mathbb of rational numbers has only finitely many rational points.

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Fermat's Last Theorem

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers,, and satisfy the equation for any integer value of greater than. Beal conjecture and Fermat's Last Theorem are abc conjecture.

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Fermat–Catalan conjecture

In number theory, the Fermat–Catalan conjecture is a generalization of Fermat's Last Theorem and of Catalan's conjecture. Beal conjecture and Fermat–Catalan conjecture are abc conjecture, conjectures, Diophantine equations and Unsolved problems in number theory.

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Gaussian integer

In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers.

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Generalization

A generalization is a form of abstraction whereby common properties of specific instances are formulated as general concepts or claims.

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Google

Google LLC is an American multinational corporation and technology company focusing on online advertising, search engine technology, cloud computing, computer software, quantum computing, e-commerce, consumer electronics, and artificial intelligence (AI).

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Henri Darmon

Henri Rene Darmon (born 22 October 1965) is a French-Canadian mathematician.

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Integer

An integer is the number zero (0), a positive natural number (1, 2, 3,...), or the negation of a positive natural number (−1, −2, −3,...). The negations or additive inverses of the positive natural numbers are referred to as negative integers.

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Jacobi–Madden equation

The Jacobi–Madden equation is the Diophantine equation proposed by the physicist Lee W. Jacobi and the mathematician Daniel J. Madden in 2008. Beal conjecture and Jacobi–Madden equation are Diophantine equations.

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Jordan Ellenberg

Jordan Stuart Ellenberg (born October 30, 1971) is an American mathematician who is a professor of mathematics at the University of Wisconsin–Madison.

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List of amateur mathematicians

This is a list of amateur mathematicians—people whose primary vocation did not involve mathematics (or any similar discipline) yet made notable, and sometimes important, contributions to the field of mathematics.

See Beal conjecture and List of amateur mathematicians

Loïc Merel

Loïc Merel (born 13 August 1965) is a French mathematician.

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Notices of the American Mathematical Society

Notices of the American Mathematical Society is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue.

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Number theory

Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions.

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Peter Norvig

Peter Norvig (born December 14, 1956) is an American computer scientist and Distinguished Education Fellow at the Stanford Institute for Human-Centered AI.

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Pierre de Fermat

Pierre de Fermat (between 31 October and 6 December 1607 – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality.

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Preda Mihăilescu

Preda V. Mihăilescu (born 23 May 1955) is a Romanian mathematician, best known for his proof of the 158-year-old Catalan's conjecture.

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Prime number

A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers.

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Prouhet–Tarry–Escott problem

In mathematics, the Prouhet–Tarry–Escott problem asks for two disjoint multisets A and B of n integers each, whose first k power sum symmetric polynomials are all equal. Beal conjecture and Prouhet–Tarry–Escott problem are Diophantine equations.

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Pythagorean quadruple

A Pythagorean quadruple is a tuple of integers,,, and, such that. Beal conjecture and Pythagorean quadruple are Diophantine equations.

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Pythagorean Triangles

Pythagorean Triangles is a book on right triangles, the Pythagorean theorem, and Pythagorean triples.

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Pythagorean triple

A Pythagorean triple consists of three positive integers,, and, such that. Beal conjecture and Pythagorean triple are Diophantine equations.

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Special case

In logic, especially as applied in mathematics, concept is a special case or specialization of concept precisely if every instance of is also an instance of but not vice versa, or equivalently, if is a generalization of.

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Sums of powers

In mathematics and statistics, sums of powers occur in a number of contexts.

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Taxicab number

In mathematics, the nth taxicab number, typically denoted Ta(n) or Taxicab(n), is defined as the smallest integer that can be expressed as a sum of two positive integer cubes in n distinct ways.

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Wacław Sierpiński

Wacław Franciszek Sierpiński (14 March 1882 – 21 October 1969) was a Polish mathematician.

See Beal conjecture and Wacław Sierpiński

References

[1] https://en.wikipedia.org/wiki/Beal_conjecture

Also known as A^x+b^y=c^z, Beal's conjecture, Mac Ganagan, Tijdeman-Zagier conjecture.

Beal conjecture, the Glossary

Table of Contents

See also

Abc conjecture

References