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Proof Of Fermat's Last Theorem For Specific Exponents
Fermat's Last Theorem is a theorem in number theory, originally stated by Pierre de Fermat in 1637 and proved by Andrew Wiles in 1995. The statement of the theorem involves an integer exponent ''n'' larger than 2. In the centuries following the initial statement of the result and before its general proof, various proofs were devised for particular values of the exponent ''n''. Several of these proofs are described below, including Fermat's proof in the case ''n'' = 4, which is an early example of the method of infinite descent. Mathematical preliminaries Fermat's Last Theorem states that no three positive integers (''a'', ''b'', ''c'') can satisfy the equation ''a''''n'' + ''b''''n'' = ''c''''n'' for any integer value of ''n'' greater than two. (For ''n'' equal to 1, the equation is a linear equation and has a solution for every possible ''a'', ''b''. For ''n'' equal to 2, the equation has infinitely many solutions, the Pythagorean triples.) Fact ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 2. The cases and have been known since antiquity to have infinitely many solutions.Singh, pp. 18–20. The proposition was first stated as a theorem by Pierre de Fermat around 1637 in the margin of a copy of '' Arithmetica''. Fermat added that he had a proof that was too large to fit in the margin. Although other statements claimed by Fermat without proof were subsequently proven by others and credited as theorems of Fermat (for example, Fermat's theorem on sums of two squares), Fermat's Last Theorem resisted proof, leading to doubt that Fermat ever had a correct proof. Consequently the proposition became known as a conjecture rather than a theorem. After 358 years of effort by mathematicians, the first successful proof was released in 1994 by Andrew Wiles and form ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Gazette
''The Mathematical Gazette'' is an academic journal of mathematics education, published three times yearly, that publishes "articles about the teaching and learning of mathematics with a focus on the 15–20 age range and expositions of attractive areas of mathematics." It was established in 1894 by Edward Mann Langley as the successor to the Reports of the Association for the Improvement of Geometrical Teaching. Its publisher is the Mathematical Association. William John Greenstreet was its editor for more than thirty years (1897–1930). Since 2000, the editor is Gerry Leversha. Editors * Edward Mann Langley: 1894-1896 * Francis Sowerby Macaulay: 1896-1897 * William John Greenstreet: 1897-1930 * Alan Broadbent: 1930-1955 * Reuben Goodstein: 1956-1962 * Edwin A. Maxwell: 1962-1971 * Douglas Quadling Douglas Arthur Quadling (1926–2015) was an English mathematician, school master and educationalist who was one of the four drivers behind the School Mathematics Project (SMP) i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetica
''Arithmetica'' ( grc-gre, Ἀριθμητικά) is an Ancient Greek text on mathematics written by the mathematician Diophantus () in the 3rd century AD. It is a collection of 130 algebraic problems giving numerical solutions of determinate equations (those with a unique solution) and indeterminate equations. Summary Equations in the book are presently called Diophantine equations. The method for solving these equations is known as Diophantine analysis. Most of the ''Arithmetica'' problems lead to quadratic equations. In Book 3, Diophantus solves problems of finding values which make two linear expressions simultaneously into squares or cubes. In book 4, he finds rational powers between given numbers. He also noticed that numbers of the form 4n + 3 cannot be the sum of two squares. Diophantus also appears to know that every number can be written as the sum of four squares. If he did know this result (in the sense of having proved it as opposed to merely conjectured it), his ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diophantus
Diophantus of Alexandria ( grc, Διόφαντος ὁ Ἀλεξανδρεύς; born probably sometime between AD 200 and 214; died around the age of 84, probably sometime between AD 284 and 298) was an Alexandrian mathematician, who was the author of a series of books called '' Arithmetica'', many of which are now lost. His texts deal with solving algebraic equations. Diophantine equations ("Diophantine geometry") and Diophantine approximations are important areas of mathematical research. Diophantus coined the term παρισότης (parisotes) to refer to an approximate equality. This term was rendered as ''adaequalitas'' in Latin, and became the technique of adequality developed by Pierre de Fermat to find maxima for functions and tangent lines to curves. Diophantus was the first Greek mathematician who recognized fractions as numbers; thus he allowed positive rational numbers for the coefficients and solutions. In modern use, Diophantine equations are usually algebraic equ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axel Thue
Axel Thue (; 19 February 1863 – 7 March 1922) was a Norwegian mathematician, known for his original work in diophantine approximation and combinatorics. Work Thue published his first important paper in 1909. He stated in 1914 the so-called word problem for semigroups or Thue problem, closely related to the halting problem.Ronald V. Book and Friedrich Otto, ''String-rewriting Systems'', Springer, 1993, , p. 36. His only known PhD student was Thoralf Skolem Thoralf Albert Skolem (; 23 May 1887 – 23 March 1963) was a Norwegian mathematician who worked in mathematical logic and set theory. Life Although Skolem's father was a primary school teacher, most of his extended family were farmers. Skolem .... The esoteric programming language Thue is named after him. Publications * * See also * * * * * * References External links * Axel Thue private archiveexists at NTNU University LibrarDorabiblioteket 1863 births 1922 deaths 20th-century Norwegian mathematicians N ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johannes Van Der Corput
Johannes Gaultherus van der Corput (4 September 1890 – 16 September 1975) was a Dutch mathematician, working in the field of analytic number theory. He was appointed professor at the University of Fribourg (Switzerland) in 1922, at the University of Groningen in 1923, and at the University of Amsterdam in 1946. He was one of the founders of the Mathematisch Centrum in Amsterdam, of which he also was the first director. From 1953 on he worked in the United States at the University of California, Berkeley, and the University of Wisconsin–Madison. He introduced the van der Corput lemma, a technique for creating an upper bound on the measure of a set drawn from harmonic analysis, and the van der Corput theorem on equidistribution modulo 1. He became member of the Royal Netherlands Academy of Arts and Sciences in 1929, and foreign member in 1953. He was a Plenary Speaker of the ICM in 1936 in Oslo. See also * van der Corput inequality * van der Corput lemma (harmonic analysi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Daniel Carmichael
Robert Daniel Carmichael (March 1, 1879 – May 2, 1967) was an American mathematician. Biography Carmichael was born in Goodwater, Alabama. He attended Lineville College, briefly, and he earned his bachelor's degree in 1898, while he was studying towards his Ph.D. degree at Princeton University. Carmichael completed the requirements for his Ph.D. in mathematics in 1911. Carmichael's Ph.D. research in mathematics was done under the guidance of the noted American mathematician G. David Birkhoff, and it is considered to be the first significant American contribution to the knowledge of differential equations in mathematics. Carmichael next taught at Indiana University from 1911 to 1915. Then he moved on to the University of Illinois, where he remained from 1915 until his retirement in 1947. Carmichael is known for his research in what are now called the Carmichael numbers (a subset of Fermat pseudoprimes, numbers satisfying properties of primes described by Fermat's Little ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karel Rychlík
Karel Rychlík (; 1885–1968) was a Czechoslovak mathematician who contributed significantly to the fields of algebra, number theory, mathematical analysis, and the history of mathematics The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments .... External linksExtensive Biography {{DEFAULTSORT:Rychlik, Karel Czechoslovak mathematicians 1885 births 1968 deaths ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Guthrie Tait
Peter Guthrie Tait FRSE (28 April 1831 – 4 July 1901) was a Scottish mathematical physicist and early pioneer in thermodynamics. He is best known for the mathematical physics textbook '' Treatise on Natural Philosophy'', which he co-wrote with Lord Kelvin, and his early investigations into knot theory. His work on knot theory contributed to the eventual formation of topology as a mathematical discipline. His name is known in graph theory mainly for Tait's conjecture. He is also one of the namesakes of the Tait–Kneser theorem on osculating circles. Early life Tait was born in Dalkeith on 28 April 1831 the only son of Mary Ronaldson and John Tait, secretary to the 5th Duke of Buccleuch. He was educated at Dalkeith Grammar School then Edinburgh Academy. He studied Mathematics and Physics at the University of Edinburgh, and then went to Peterhouse, Cambridge, graduating as senior wrangler and first Smith's prizeman in 1852. As a fellow and lecturer of his college he remai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gabriel Lamé
Gabriel Lamé (22 July 1795 – 1 May 1870) was a French mathematician who contributed to the theory of partial differential equations by the use of curvilinear coordinates, and the mathematical theory of elasticity (for which linear elasticity and finite strain theory elaborate the mathematical abstractions). Biography Lamé was born in Tours, in today's ''département'' of Indre-et-Loire. He became well known for his general theory of curvilinear coordinates and his notation and study of classes of ellipse-like curves, now known as Lamé curves or superellipses, and defined by the equation: : \left, \,\,\^n + \left, \,\,\^n =1 where ''n'' is any positive real number. He is also known for his running time analysis of the Euclidean algorithm, marking the beginning of computational complexity theory. Using Fibonacci numbers, he proved that when finding the greatest common divisor of integers ''a'' and ''b'', the algorithm runs in no more than 5''k'' steps, where ''k'' is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adrien-Marie Legendre
Adrien-Marie Legendre (; ; 18 September 1752 – 9 January 1833) was a French mathematician who made numerous contributions to mathematics. Well-known and important concepts such as the Legendre polynomials and Legendre transformation are named after him. Life Adrien-Marie Legendre was born in Paris on 18 September 1752 to a wealthy family. He received his education at the Collège Mazarin in Paris, and defended his thesis in physics and mathematics in 1770. He taught at the École Militaire in Paris from 1775 to 1780 and at the École Normale Supérieure, École Normale from 1795. At the same time, he was associated with the Bureau des Longitudes. In 1782, the Prussian Academy of Sciences, Berlin Academy awarded Legendre a prize for his treatise on projectiles in resistant media. This treatise also brought him to the attention of Lagrange. The ''Académie des sciences'' made Legendre an adjoint member in 1783 and an associate in 1785. In 1789, he was elected a Fellow of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christian Goldbach
Christian Goldbach (; ; 18 March 1690 – 20 November 1764) was a German mathematician connected with some important research mainly in number theory; he also studied law and took an interest in and a role in the Russian court. After traveling around Europe in his early life, he landed in Russia in 1725 as a professor at the newly founded Saint Petersburg Academy of Sciences. Goldbach jointly led the Academy in 1737. However, he relinquished duties in the Academy in 1742 and worked in the Russian Ministry of Foreign Affairs until his death in 1764. He is remembered today for Goldbach's conjecture and the Goldbach–Euler Theorem. He had a close friendship with famous mathematician Leonard Euler, serving as inspiration for Euler's mathematical pursuits. Biography Early life Born in the Duchy of Prussia's capital Königsberg, part of Brandenburg-Prussia, Goldbach was the son of a pastor. He studied at the Royal Albertus University. After finishing his studies he went on long ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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