Fermat's last theorem

Fermat's last theorem
/fer mahz"/, Math.
the unproved theorem that the equation xn + yn = zn has no solution for x, y, z nonzero integers when n is greater than 2.
[1860-65; named after P. de FERMAT]

* * *

Statement that there are no natural numbers x, y, and z such that xn + yn = zn, in which n is a natural number greater than 2.

About this, Pierre de Fermat wrote in 1637 in his copy of Diophantus's Arithmetica, "I have discovered a truly remarkable proof but this margin is too small to contain it." Although the theorem was subsequently shown to be true for many specific values of n, leading to important mathematical advances in the process, the difficulty of the problem soon convinced mathematicians that Fermat never had a valid proof. In 1995 the British mathematician Andrew Wiles (b. 1953) and his former student Richard Taylor (b. 1962) published a complete proof, finally solving one of the most famous of all mathematical problems.

* * *

also called  Fermat's great theorem 

      the statement that there are no natural numbers (1, 2, 3, …) x, y, and z such that xn + yn = zn, in which n is a natural number greater than 2. For example, if n = 3, Fermat's theorem states that no natural numbers x, y, and z exist such that x3 + y 3 = z3 (i.e., the sum of two cubes is not a cube). In 1637 the French mathematician Pierre de Fermat (Fermat, Pierre de) wrote in his copy of the Arithmetica by Diophantus of Alexandria (c. AD 250), “I have discovered a truly remarkable proof [of this theorem] but this margin is too small to contain it.” For centuries mathematicians were baffled by this statement, for no one could prove or disprove Fermat's theorem. Proofs for many specific values of n were devised, however, and by 1993, with the help of computers, it was confirmed for all n < 4,000,000. Using sophisticated tools from algebraic geometry, the English mathematician Andrew Wiles (Wiles, Andrew John), with help from his former student Richard Taylor, devised a proof of Fermat's last theorem that was published in 1995 in the journal Annals of Mathematics.

* * *


Universalium. 2010.

Игры ⚽ Поможем написать реферат

Look at other dictionaries:

  • Fermat's Last Theorem — is the name of the statement in number theory that:: It is impossible to separate any power higher than the second into two like powers,or, more precisely:: If an integer n is greater than 2, then the equation a^n + b^n = c^n has no solutions in… …   Wikipedia

  • Fermat's Last Theorem in fiction — The famous problem in number theory known as Fermat s Last Theorem has repeatedly received attention in fiction and popular culture.* In The Royale , an episode of , Captain Picard states that the theorem had gone unsolved for 800 years. At the… …   Wikipedia

  • Fermat's Last Theorem — /fɛəˈmaz/ (say fair mahz) noun the long unproven theorem that the equation xn + yn = zn has no positive integer solutions for x, y, z when n is greater than 2. {from the fact that this was the last of the theorems of Pierre de Fermat which… …  

  • Fermat's last theorem — noun Etymology: Pierre de Fermat Date: 1847 a theorem in number theory: the equation xⁿ + yⁿ = zⁿ has no solutions when x, y, z, and n are all positive integers and n is greater than 2 …   New Collegiate Dictionary

  • Fermat's last theorem — noun Mathematics the theorem (proved in 1995) that if n is an integer greater than 2, the equation xn + yn = zn has no positive integral solutions. Origin C19: named after the 17th cent. French mathematician Pierre de Fermat …   English new terms dictionary

  • Fermat's last theorem — /fer mahz /, Math. the unproved theorem that the equation xn + yn = zn has no solution for x, y, z nonzero integers when n is greater than 2. [1860 65; named after P. de FERMAT] …   Useful english dictionary

  • Fermat's little theorem — (not to be confused with Fermat s last theorem) states that if p is a prime number, then for any integer a , a^p a will be evenly divisible by p . This can be expressed in the notation of modular arithmetic as follows::a^p equiv a pmod{p},!A… …   Wikipedia

  • The Last Theorem — infobox Book | name = The Last Theorem title orig = translator = image caption = author = Arthur C. Clarke Frederik Pohl illustrator = cover artist = country = language = English series = genre = Science Fiction publisher = Del Rey Books release… …   Wikipedia

  • Proofs of Fermat's little theorem — This article collects together a variety of proofs of Fermat s little theorem, which states that:a^p equiv a pmod p ,!for every prime number p and every integer a (see modular arithmetic). Simplifications Some of the proofs of Fermat s little… …   Wikipedia

  • Fermat's Enigma — is a book which explains Fermat s last theorem, beginning with Pythagoras up until its proof by Andrew Wiles, written by Simon Singh and published in 1998 …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”