Pierre de Fermat's conjecture written in the margin of his copy of Arithmetica proved to be one of the most intriguing and enigmatic mathematical problems ever devised.

Problem II.8 in the 1621 edition of the Arithmetica of Diophantus. On the right is the famous margin which was too small to contain Fermat's alleged proof of his last theorem.

Fermat's last theorem states that: In the public domain by age This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ... In the public domain by age This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ... Pierre de Fermat Pierre de Fermat IPA: (August 17, 1601–January 12, 1665) was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to modern calculus. ... Image File history File links Download high resolution version (911x1520, 559 KB) Summary Work by Diophantus (died in about 280 B.C.), translated from Greek into Latin by Claude Gaspard Bachet de Méziriac. ... Image File history File links Download high resolution version (911x1520, 559 KB) Summary Work by Diophantus (died in about 280 B.C.), translated from Greek into Latin by Claude Gaspard Bachet de Méziriac. ... Title page of the 1621 edition of Diophantus Arithmetica, translated into Latin by Claude Gaspard Bachet de Méziriac. ...

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 aⁿ + bⁿ = cⁿ has no solutions in non-zero integers a, b, and c.

In 1637 Fermat wrote, in his copy of Claude-Gaspar Bachet's translation of the famous Arithmetica of Diophantus, "I have a truly marvelous proof of this proposition which this margin is too narrow to contain." (Original Latin: "Cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet.") The integers are commonly denoted by the above symbol. ... Claude Gaspard Bachet de Méziriac (October 9, 1581 - February 26, 1638) was a French mathematician born in Bourg-en-Bresse. ... Arithmetica, an ancient text on mathematics written by classical period Greek mathematician Diophantus in the second century AD is a collection of 130 algebra problems giving numerical solutions of determinate equations (those with a unique solution), and indeterminate equations. ... Title page of the 1621 edition of Diophantus Arithmetica, translated into Latin by Claude Gaspard Bachet de Méziriac. ... In mathematics, a proof is a demonstration that, assuming certain axioms, some statement is necessarily true. ... For other uses, see Latin (disambiguation). ...

Fermat's last theorem is strikingly different and much more difficult to prove than the analogous problem for n = 2, for which there are infinitely many integer solutions called Pythagorean triples (and the closely related Pythagorean theorem has many elementary proofs). The fact that the problem's statement is understandable by schoolchildren makes it all the more frustrating, and it has probably generated more incorrect proofs than any other problem in the history of mathematics. No correct proof was found for 357 years, when a proof was finally published by Andrew Wiles in 1994. The term "last theorem" resulted because all the other theorems proposed by Fermat were eventually proved or disproved, either by his own proofs or by other mathematicians, in the two centuries following their proposition. The Pythagorean theorem: a2 + b2 = c2 A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. ... In mathematics, the Pythagorean theorem (AmE) or Pythagoras theorem (BrE) is a relation in Euclidean geometry among the three sides of a right triangle. ... For the French mathematician with work in the area of elliptic curves, see André Weil. ...

Fermat's last theorem is one of the most famous theorems in the history of mathematics, familiar to nigh every mathematician, and had achieved a recognizable status in popular culture prior to its proof. The avalanche of media coverage generated by the resolution of Fermat's last theorem was the first of its kind, including worldwide newspaper accounts and various popularizations in books and a PBS NOVA special, The Proof. Look up theorem in Wiktionary, the free dictionary. ... For a timeline of events in mathematics, see timeline of mathematics. ... Not to be confused with Public Broadcasting Services in Malta. ... Nova is a popular science television series from the USA produced by WGBH and can be seen on PBS and in more than 100 countries. ...

The 1670 edition of Arithmetica is already annotated with the comment of Fermat which became known as his "last theorem".

Image File history File links Download high resolution version (978x1520, 271 KB) Summary Work by Diophantus (died in about 280 B.C.), with additions by Pierre de Fermat (died in 1665). ... Image File history File links Download high resolution version (978x1520, 271 KB) Summary Work by Diophantus (died in about 280 B.C.), with additions by Pierre de Fermat (died in 1665). ...

Fermat's last theorem from a comment in a margin

In problem II.8 of his Arithmetica, Diophantus asks how to split a given square number into two other squares (in modern notation, given a rational number k, find u and v, both rational, such that k² = u² + v²), and shows how to solve the problem for k = 4. Around 1640, Fermat wrote in the margin next to this problem in his copy of the Arithmetica:^[1] Arithmetica, an ancient text on mathematics written by classical period Greek mathematician Diophantus in the second century AD is a collection of 130 algebra problems giving numerical solutions of determinate equations (those with a unique solution), and indeterminate equations. ... Title page of the 1621 edition of Diophantus Arithmetica, translated into Latin by Claude Gaspard Bachet de Méziriac. ...

While Fermat's original margin note was lost with his copy of Arithmetica, around 1670, his son produced a new edition of the book augmented with his father's comments. The note eventually became known as Fermat's last theorem, as it became the last of Fermat's asserted theorems to remain unproven.

In the case n = 2, it was already known by the ancient Chinese, Indians, Greeks, and Babylonians that the Diophantine equation a² + b² = c² (linked with the Pythagorean theorem) has integer solutions, such as (3,4,5) (3² + 4² = 5²) and (5,12,13). These solutions are known as Pythagorean triples, and there exist infinitely many of them, even excluding solutions for which a, b and c have a common divisor (that is, when the entire equation is multiplied by the square of an integer). Fermat's last theorem is an extension of this problem to higher powers n, and states that no such solution exists when the exponent 2 is replaced by a larger integer. Babylonian mathematics refers to any mathematics of the peoples of Mesopotamia, from the days of the early Sumerians to the fall of Babylon in 539 BC. In contrast to the sparsity of sources in Egyptian mathematics, our knowledge of Babylonian mathematics is derived from some 400 clay tablets unearthed since... In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. ... In mathematics, the Pythagorean theorem (AmE) or Pythagoras theorem (BrE) is a relation in Euclidean geometry among the three sides of a right triangle. ... The Pythagorean theorem: a2 + b2 = c2 A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. ... In mathematics, a divisor of an integer n, also called a factor of n, is an integer which evenly divides n without leaving a remainder. ...

History of the proof

Leonhard Euler by Emanuel Handmann.

A special case of Fermat's last theorem for n = 3 was first stated by Abu-Mahmud al-Khujandi in the 10th century, but his attempted proof of the theorem was incorrect.^[2] Image File history File links Picture of Leonhard Euler by Emanuel Handmann. ... Image File history File links Picture of Leonhard Euler by Emanuel Handmann. ... Leonhard Paul Euler (pronounced Oiler; IPA ) (April 15, 1707 – September 18 [O.S. September 7] 1783) was a pioneering Swiss mathematician and physicist, who spent most of his life in Russia and Germany. ... Jakob Emanuel Handmann, born 1718 in Basel, died 1781 in Bern. ... Abu Mahmud Hamid ibn al-Khidr Al-Khujandi was a Persian (Tajik) astronomer and mathematician who lived in the late 10th century and helped build an observatory near in what is now Ray, Iran near Tehran. ... As a means of recording the passage of time, the 10th century was that century which lasted from 901 to 1000. ...

The first case of Fermat's last theorem to be proven, by Fermat himself, was the case n = 4 using the method of infinite descent. Using a similar method, Euler proved the theorem for n = 3; although his published proof contains some errors, the needed assertions could be established with work Euler himself had proven elsewhere. While his original method contained a flaw, it generated a great deal of research about the theorem. Over the following centuries, the theorem was established for many other special exponents n (or classes of exponents), but the general case remained elusive. In mathematics, a proof by infinite descent is a particular kind of proof by mathematical induction. ... Leonhard Euler aged 49 (oil painting by Emanuel Handmann, 1756) Leonhard Euler (April 15, 1707 - September 18, 1783) (pronounced oiler) was a Swiss mathematician and physicist. ...

The case n = 5 was proved by Dirichlet and Legendre in 1825 using a generalisation of Euler's proof for n = 3. The proof for the next prime number (it is enough to prove the theorem for prime numbers: see below), n = 7 was found 15 years later by Gabriel Lamé in 1839. Unfortunately, this demonstration was relatively long and unlikely to be generalised to higher numbers. From this point, mathematicians started to demonstrate the theorem for classes of exponents, instead of individual numbers, and develop more general results related to the theorem. Johann Peter Gustav Lejeune Dirichlet (February 13, 1805 - May 5, 1859) was a German mathematician credited with the modern formal definition of a function. ... Adrien-Marie Legendre (September 18, 1752–January 10, 1833) was a French mathematician. ... In mathematics, a prime number (or a prime) is a natural number which has exactly two distinct natural number divisors: 1 and itself. ... Gabriel Lamé (July 22, 1795, Tours, France - May 1, 1870, Paris, France) was a French mathematician. ...

These general ideas can be traced back to a novel approach introduced by Sophie Germain. Rather than proving that there were no solutions to a given value n, she demonstrated that if there was a solution, a certain condition would have to apply. This insight was already used in the proof of Fermat's last theorem for the case n = 5. In 1847, Kummer proved that the theorem was true for all regular prime numbers (which include all prime numbers between 2 and 100 except for 37, 59 and 67). Sophie Germain Marie-Sophie Germain (April 1, 1776 – June 27, 1831), born to a middle-class merchant family in Paris, France, was a French mathematician. ... Ernst Eduard Kummer (29 January 1810 in Sorau, Brandenburg, Prussia - 14 May 1893 in Berlin, Germany) was a German mathematician. ... In mathematics, regular primes are a certain kind of prime numbers. ...

In 1823 and then in 1850, the French Academy of Sciences offered a prize for a correct proof. This initiative only caused a wave of thousands of mathematical misadventures. A third prize was offered in 1883 by the Academy of Brussels. In 1908, the German physician and amateur mathematician Paul Freidrich Wolfskehl bequeathed 100,000 marks to the Göttingen Academy of Sciences to be offered as a prize for a complete proof of Fermat's last theorem. As a result, from 1908-1911, a flood of over 1000 incorrect proofs were presented. According to mathematical historian Howard Eves: Louis XIV visiting the Académie in 1671 The French Academy of Sciences (Académie des sciences) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. ... Paul Friedrich Wolfskehl (1856-1906) was a mathematician born in Darmstadt. ... Howard Whitley Eves (10 January 1911 New Jersey - 6 June 2004) was an American mathematician, known for his work in geometry and the history of mathematics. ...

"Fermat's last theorem, has the peculiar distinction of being the mathematical problem for which the greatest number of incorrect proofs have been published".

Andrew Wiles

Image File history File linksMetadata Download high resolution version (2710x1800, 499 KB) http://www. ... Image File history File linksMetadata Download high resolution version (2710x1800, 499 KB) http://www. ... For the French mathematician with work in the area of elliptic curves, see André Weil. ...

Elliptic curves and Wiles' proof

The history of the proof of Fermat's last theorem begins in the late 1960s, when Yves Hellegouarch came up with an idea of associating to any solution (a,b,c) of Fermat's equation a completely different mathematical object: an elliptic curve. The curve consists of all points in the plane whose coordinates (x,y) satisfy the relation In mathematics, an elliptic curve is a plane curve defined by an equation of the form y2 = x3 + a x + b, which is non-singular; that is, its graph has no cusps or self-intersections. ...

y² = x(x − a^p)(x + b^p).

Such an elliptic curve would enjoy very special properties, which are due to the appearance of high powers of integers in its equation and the fact that a^p + b^p = c^p is a pth power as well. Gerhard Frey had an insight that such a curve would be so special that it would contradict a certain conjecture about elliptic curves which is now called the Taniyama–Shimura conjecture. This conjecture says that each elliptic curve with rational coefficients can be constructed in an entirely different way, not by giving its equation but by using modular functions to parametrize coordinates x and y of the points on it. Thus, according to the conjecture, any elliptic curve over Q would have to be a modular elliptic curve, yet if a solution to Fermat's equation with non-zero a, b, c and p greater than 2 existed, the corresponding curve would not be modular, resulting in a contradiction. The link between the Fermat's last theorem and the Taniyama–Shimura conjecture is a little subtle: in order to derive the former from the latter, one needs to know a bit more, or as mathematicians would have it, "an epsilon more". This extra piece of information was identified by Jean-Pierre Serre and became known as the epsilon conjecture. Serre's main interest was in an even more ambitious conjecture, Serre's conjecture on modular Galois representations, which would imply the Taniyama–Shimura conjecture. Although in the preceding twenty or thirty years a lot of evidence had been accumulated to form conjecture about elliptic curves, the main reason to believe that these various conjectures were true lay not in the numerical confirmations, but in a remarkably coherent and attractive mathematical picture that they presented. Moreover, it could have happened that one or more of these conjectures were actually false (for example, Serre's conjecture is still wide open), and yet Fermat's last theorem were nonetheless true. That would simply mean that one should try a different approach. Gerhard Frey is a German mathematician, known for his work in number theory. ... In mathematics, the modularity theorem establishes an important connection, between elliptic curves over the field of rational numbers and modular forms, certain analytic functions introduced in 19th century mathematics. ... In mathematics, modular functions are certain kinds of mathematical functions mapping complex numbers to complex numbers. ... In mathematics, the differential geometry of curves provides definitions and methods to analyze smooth curves in Riemannian manifolds and Pseudo-Riemannian manifolds (and in particular in Euclidean space) using differential and integral calculus. ... In mathematics, a modular curve is a Riemann surface, or corresponding algebraic curve, constructed as H/Γ where H is the upper half-plane in the complex numbers, and Γ is a Fuchsian group acting on H, with Γ a subgroup of the modular group of integral 2×2 matrices. ... Jean-Pierre Serre (born September 15, 1926) is one of the leading mathematicians of the twentieth century, active in algebraic geometry, number theory and topology. ... In number theory, Serres epsilon conjecture stated a property of Galois representations associated with modular forms which was proven by Ken Ribet in the summer of 1986, in in a significant step towards the proof of Fermats Last Theorem. ... In mathematics, Jean-Pierre Serre conjectured the following result regarding two-dimensional Galois representations. ...

In the summer of 1986, Ken Ribet succeeded in proving the epsilon conjecture. (His article was published in 1990.) He demonstrated that, just as Frey had anticipated, a special case of the Taniyama–Shimura conjecture (still unproven at the time), together with the now proven epsilon conjecture, implies the Fermat's last theorem. Thus if the Taniyama–Shimura conjecture holds for a class of elliptic curves called semistable elliptic curves, then the Fermat's last theorem would be true. Kenneth Alan Ken Ribet is an American mathematician, currently a professor of mathematics at the University of California, Berkeley. ... In mathematics, a semistable elliptic curve in diophantine geometry is an elliptic curve that has bad reduction only of multiplicative type. ...

After learning about Ribet's work, Andrew Wiles set out to prove that every semistable elliptic curve is modular. He did so in almost complete secrecy, working for a full seven years with minimal outside help. Over the course of three lectures delivered at Isaac Newton Institute for Mathematical Sciences on June 21, 22, and 23 of 1993, Wiles announced his proof of the Taniyama–Shimura conjecture, and hence of the Fermat's last theorem. Wiles drew upon a wide variety of methods in the proof, some of them having been developed especially for this occasion. For the French mathematician with work in the area of elliptic curves, see André Weil. ... Opened in 1992, the Isaac Newton Institute for Mathematical Sciences is the United Kingdoms de facto national research institute for mathematics and theoretical physics. ...

Nick Katz

Although Wiles had reviewed his argument beforehand with a Princeton colleague, Nick Katz, he soon discovered that the proof contained a gap. There was an error in a critical portion of the proof which gave a bound for the order of a particular group. Wiles and his former student Richard Taylor spent almost a year trying to repair the proof, under the close scrutiny of the media and the mathematical community. In September 1994, they were able to complete the proof by using a very novel approach in the troublesome part of the argument. Taylor and others would go on to prove the general form of the Taniyama–Shimura conjecture, now frequently called the modularity theorem, which applies to all elliptic curves over Q, not just the semistable curves that were relevant for the proof of Fermat's last theorem. Image File history File linksMetadata Download high resolution version (2710x1800, 347 KB) nick katz http://www. ... Image File history File linksMetadata Download high resolution version (2710x1800, 347 KB) nick katz http://www. ... Nick Katz (Nicholas M. Katz) is an American mathematician, working in the fields of algebraic geometry, particularly on p-adic methods, monodromy and moduli problems, and number theory. ... Nick Katz (Nicholas M. Katz) is an American mathematician, working in the fields of algebraic geometry, particularly on p-adic methods, monodromy and moduli problems, and number theory. ... Richard Taylor (born 19 May 1962) is a British mathematician working in the field of number theory. ... In mathematics, the modularity theorem establishes an important connection between elliptic curves over the field of rational numbers and modular forms, certain analytic functions introduced in 19th century mathematics. ...

Taylor and Wiles's proof is extremely technical in that it relies on the mathematical techniques developed in the twentieth century, most of which would be totally alien to mathematicians who had worked on Fermat's last theorem only a century earlier. Fermat's alleged "marvelous proof", on the other hand, would have had to be fairly elementary, given the state of the mathematical knowledge at the time. And in fact, most mathematicians and historians of science doubt that Fermat had a valid proof of his theorem for all exponents n.

Mathematics of the theorem and its proof

Fermat's last theorem needs only to be proven for n = 4 and prime numbers greater than 2. If n > 2 is not a prime number or 4, it can be either a power of 2 or not. In the first case the number 4 is a factor of n, otherwise there is an odd prime number among its factors. In any case let any such factor be p, and let m be n / p. Now we can express the equation as (a^m)^p + (b^m)^p = (c^m)^p. If we can prove the case with exponent p, exponent n is simply a subset of that case. In mathematics, a prime number (or a prime) is a natural number which has exactly two distinct natural number divisors: 1 and itself. ...

Fermat's last theorem stimulated the development of a great deal of modern ring theory. In particular, the notion of an ideal and the ideal class group grew out of Kummer's work on the theorem, and his proof of it for regular primes. In mathematics, ring theory is the study of rings, algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers. ... In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring. ... In mathematics the theory of algebraic number fields gives rise to a finite abelian group constructed from each such field, its ideal class group. ...

In 1977, Guy Terjanian proved that if p is an odd prime number, and the natural numbers x, y and z satisfy x^2p + y^2p = z^2p, then 2p must divide x or y. Guy Terjanian is a French mathematician. ...

The Mordell conjecture, proven by Gerd Faltings in 1983, implies that for any n > 2, there are at most finitely many coprime integers a, b and c with aⁿ + bⁿ = cⁿ. In number theory, the Mordell conjecture stated a basic result regarding the rational number solutions to Diophantine equations. ... Gerd Faltings, June 2006 Gerd Faltings (born July 28, 1954 in Gelsenkirchen-Buer) is a German Lutheran mathematician known for his work in arithmetic algebraic geometry. ... Coprime - Wikipedia /**/ @import /skins-1. ... The integers are commonly denoted by the above symbol. ...

The Taniyama–Shimura conjecture states that every elliptic curve can be parametrised by a rational map with integer coefficients using the classical modular curve; that is, all elliptic curves (over the rationals) can be described by modular forms. In mathematics, the modularity theorem establishes an important connection, between elliptic curves over the field of rational numbers and modular forms, certain analytic functions introduced in 19th century mathematics. ... In number theory, the classical modular curve is an irreducible plane algebraic curve given by an equation Φn(x, y)=0, where for the j-invariant j(Ï„), x=j(n Ï„), y=j(Ï„) is a point on the curve. ... A modular form is an analytic function on the upper half plane satisfying a certain kind of functional equation and growth condition. ...

On the other hand Ribet's theorem shows that for any nontrivial solution to Fermat's equation, aⁿ + bⁿ = cⁿ, the semistable elliptic curve of Hellegouarch and Frey, defined by In mathematics, a semistable elliptic curve in diophantine geometry is an elliptic curve that has bad reduction only of multiplicative type. ...

y² = x(x − aⁿ)(x + bⁿ),

is not modular. Fermat's last theorem therefore follows from the Taniyama–Shimura conjecture.

The proof of this theorem for semistable elliptic curves by Wiles (and, in part, Taylor) uses many techniques from algebraic geometry and number theory, and has many ramifications in these branches of mathematics. As well as standard constructions of modern algebraic geometry, using the category of schemes and Iwasawa theory, the proof involved the development ideas from Barry Mazur on deformations of Galois representations and contributed to the Langlands program. Algebraic geometry is a branch of mathematics which, as the name suggests, combines techniques of abstract algebra, especially commutative algebra, with the language and the problematics of geometry. ... In mathematics, categories allow one to formalize notions involving abstract structure and processes that preserve structure. ... In mathematics, a scheme is an important concept connecting the fields of algebraic geometry, commutative algebra and number theory. ... In number theory, Iwasawa theory is a Galois module theory of ideal class groups, initiated by Kenkichi Iwasawa, in the 1950s, as part of the theory of cyclotomic fields. ... Barry Mazur (born December 19, 1937) is a professor of mathematics at Harvard University. ... In mathematics, and in particular in algebraic number theory, a Galois module is a module for a Galois group — equivalently for a Galois group G and a group ring R[G] of G with respect to some ring R, it is some R[G]-module M. In that general... In mathematics, the Langlands program is a web of far-reaching and influential conjectures that connect number theory and the representation theory of certain groups. ...

Generalizations and similar equations

Many Diophantine equations have a form similar to the equation of Fermat's last theorem, without necessarily sharing its properties. In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. ...

For example, it is known that there are infinitely many positive integers x, y, and z such that xⁿ + yⁿ = z^m in which n and m are any relatively prime natural numbers. In mathematics, the integers a and b are said to be coprime or relatively prime if and only if they have no common factor other than 1 and −1, or equivalently, if their greatest common divisor is 1. ...

In fiction

• In "The Royale", an episode of Star Trek: The Next Generation, Captain Picard states that the theorem had gone unsolved for 800 years. At the end of the episode Captain Picard says, "Like Fermat's theorem, it is a puzzle we may never solve." Wiles' proof was released five years after the particular episode aired. This was subsequently mentioned in a Star Trek: Deep Space Nine episode called "Facets" during June 1995 in which Jadzia Dax comments that one of her previous hosts, Tobin Dax, had "the most original approach to the proof since Wiles over 300 years ago." [1] This reference was generally understood by fans to be a retroactive continuity for "The Royale".

• A sum, proved impossible by the theorem, appears in an episode of The Simpsons, "Treehouse of Horror VI". In the three-dimensional world in "Homer³", the equation 1782¹² + 1841¹² = 1922¹² is visible, just as the dimension begins to collapse. The joke is that the twelfth root of the sum does evaluate to 1922 due to rounding errors when entered into most handheld calculators; notice that the left hand side is odd, while 1922¹² is even, so the equality cannot hold. The values agree to 9 of 40 decimal digits. A second 'counterexample' appeared in a later episode, "The Wizard of Evergreen Terrace": 3987¹² + 4365¹² = 4472¹². These agree to 10 of 44 decimal digits, but notice simple divisibility rules show 3987 and 4365 are divisible by 9 so that a sum of their powers is also. A similar rule reveals 4472 is not divisible by 3, so that this cannot hold either.

• In Tom Stoppard's play Arcadia, Septimus Hodge poses the problem of proving Fermat's last theorem to the precocious Thomasina Coverly (who is perhaps a mathematical prodigy), in an attempt to keep her busy. Thomasina's (perhaps perceptive) response is simple—that Fermat had no proof, and it was a joke to drive posterity mad.

• Arthur Porges' short story, "The Devil and Simon Flagg", features a mathematician who bargains with the Devil that the latter cannot produce a proof of Fermat's last theorem within twenty-four hours. The devil is not successful. The story was first published in 1954 in The Magazine of Fantasy and Science Fiction.

• Fermat's equation also appeared in the movie Bedazzled with Elizabeth Hurley and Brendan Fraser. Hurley played the devil who, in one of her many forms, appeared as a school teacher. In this particular scene the blackboard behind her reads: "Tonight's homework: Prove aⁿ + bⁿ = cⁿ".
• In one of the Rama series books the problem is supposed to have been solved very simply and elegantly (probably the way Fermat himself had intended it) by a young girl.

• In Elizabeth Kay's book Jinx on the Divide the main character intrigues a mythological griffin with the theorem; the griffin solves it in less than a week.

• In the online game the Lost Experience, which is directly related to the television series Lost, the equation is said to have been originally solved by a scientist by the name of Enzo Vallenzetti (also the creator of the Vallenzetti Equation) sometime in the late 1960s. However due to his eccentric nature, after having the proof verified by his colleagues, Vallenzetti is said to have burned his work so that, according to his assistant, "others could have as much fun solving it as he did".

• In the book The Oxford Murders by Guillermo Martinez, Wiles's announcement in Cambridge of his proof of Fermat's last theorem forms a peripheral part of the action.

• In the book The Light of Other Days by Arthur C. Clarke and Stephen Baxter technology was developed which allowed the general public to look back into time. A 12 year old was able to read Fermat's actual proof and present it in the present time.

• The rock metal band KINETO has a song entitled "Theorem" that describes Fermat's last theorem.

• In Jasper Fforde's book First Among Sequels, 9 year-old Tuesday Next, seeing the equation on the sixth-form's math classroom's chalkboard, and thinking it homework, solves it quite simply.

• In Stieg Larsson's 2006 book Flickan som lekte med elden, the main character Lisbeth Salander is mesmerized by the Theorem. She spends a great deal of time trying to prove it herself, stubbornly avoiding the presented proof.

The Royale is the name of an episode from the second season of Star Trek: The Next Generation. ... The title as it appeared in most episodes opening credits. ... Jean-Luc Picard is a fictional human Star Trek character portrayed by actor Patrick Stewart. ... Jean-Luc Picard is a fictional human Star Trek character portrayed by actor Patrick Stewart. ... Space station Star Trek: Deep Space Nine (ST:DS9 or STDS9 or DS9 for short) is a science fiction television series produced by Paramount and set in the Star Trek universe. ... Facets is the penultimate episode in the third season of Star Trek: Deep Space Nine. ... Jadzia Dax, played by Terry Farrell, is a main character in television series Star Trek: Deep Space Nine. ... In the television series Star Trek: Deep Space Nine Tobin Dax was a noted engineer and mathematician in Trill history, Tobin was the second host of the Dax symbiont. ... Retroactive continuity – commonly contracted to the portmanteau word retcon – refers to the act of changing previously established details of a fictional setting, often without providing an explanation for the changes within the context of that setting. ... Simpsons redirects here. ... Treehouse of Horror VI is the sixth episode of The Simpsons seventh season, as well as the sixth Halloween episode. ... The Wizard of Evergreen Terrace is the second episode of the tenth season of The Simpsons. ... A divisibility rule is a method that can be used to determine whether a number is evenly divisible by other numbers. ... Sir Tom Stoppard, OM, CBE (born as Tomáš Straussler on July 3, 1937)[1] is an Academy Award winning British playwright of more than 24 plays. ... Arcadia is a play by Tom Stoppard which first opened at the Royal National Theatre in London on 13 April 1993 and has played at many theatres since. ... Arthur Porges (born August 20, 1915) is a pulp magazine author of numerous short stories, most notably in the 1950s and 60s. ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... Satan frozen at the center of Cocytus, the ninth circle of Hell in Dantes Inferno. ... F&SF April 1971, special Poul Anderson issue. ... Elizabeth Jane Hurley (born 10 June 1965) is an English actress, fashion model, producer and designer. ... This article needs additional references or sources for verification. ... Rendezvous with Rama is a novel by Arthur C. Clarke first published in 1972. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... The Divide trilogy by Elizabeth Kay The Divide trilogy describes the adventures of Felix Sanders in an alternate universe where myth is reality and reality is myth. ... Statue of a griffin at St. ... The Lost Experience was an alternate reality game that was part of the ABC television drama Lost. ... Lost is an Emmy Award and Golden Globe-winning American serial drama television series that follows the lives of plane crash survivors on a mysterious tropical island, after a passenger jet flying between Australia and the United States crashes somewhere in the South Pacific. ... The Oxford Murders is a thriller film adapted from award-winning novel by the Argentinean writer Guillermo Martinez, directed by Álex de la Iglesia and starring John Hurt and Elijah Wood. ... Guillermo Martínez (born 29 July 1962) is an Argentinian writer. ... The Light of Other Days is a 2000 science fiction novel by Arthur C. Clarke and Stephen Baxter. ... Sir Arthur Charles Clarke, CBE (born 16 December 1917) is a British science-fiction author and inventor, most famous for his novel 2001: A Space Odyssey, and for collaborating with director Stanley Kubrick on the film of the same name. ... Stephen Baxter (born in Liverpool, 13 November 1957) is a British hard science fiction author. ... Jasper Fforde (born in London on 11 January 1961) is a novelist and aviator living in Wales. ... First Among Sequels is the announced name of the fifth novel in the Thursday Next series written by Jasper Fforde. ... Animal magnetism (French: magnétisme animal) is also known eponymously as mesmerism after Franz Mesmer who postulated the existence of a magnetic fluid or ethereal medium as a therapeutic agent. ...

See also

Wikibooks has more on the topic of

Fermat's last theorem

• Euler's conjecture
• Fermat's little theorem
• Sophie Germain prime
• Wall-Sun-Sun prime
• Beal's conjecture

Image File history File links Wikibooks-logo-en. ... Wikibooks logo Wikibooks, previously called Wikimedia Free Textbook Project and Wikimedia-Textbooks, is a wiki for the creation of books. ... Eulers conjecture is a conjecture in mathematics related to Fermats last theorem which was proposed by Leonhard Euler in 1769. ... Fermats little theorem (not to be confused with Fermats last theorem) states that if p is a prime number, then for any integer a, This means that if you start with a number, initialized to 1, and repeatedly multiply, for a total of p multiplications, that number by... A prime number p is called a Sophie Germain prime if 2p + 1 is also prime. ... In mathematics, a Wall-Sun-Sun prime is a certain kind of prime number. ... Beals conjecture is a conjecture in number theory proposed by the Texas billionaire and mathematical amateur Andrew Beal. ...

Notes

Claude Gaspard Bachet de Méziriac (October 9, 1581 - February 26, 1638) was a French mathematician born in Bourg-en-Bresse. ... The MacTutor history of mathematics archive is a website hosted by University of St Andrews in Scotland. ...

References

• O'Connor, J. J. and Robertson, E. F. (1996). Fermat's last theorem. The history of the problem. Retrieved Aug. 5, 2004.
• Faltings, Gerd (1995). The Proof of Fermat's Last Theorem by R. Taylor and A. Wiles, Notices of the AMS 42 (7), pp. 743–746.
• Singh, Simon (paperback, 1998). Fermat's Enigma. Anchor Books, New York. ISBN 0385493622 (previously published in 1997 under the title "Fermat's Last Theorem" by Fourth Estate, ISBN 1857025210).
• Taylor, Richard and Wiles, Andrew (1995). Ring theoretic properties of certain Hecke algebras, Annals of Mathematics 141 (3), pp. 553–572.
• Terjanian, G. (1977), Sur l'équation x^2p + y^2p = z^2p, Comptes rendus hebdomadaires des séances de l'Académie des sciences. Série A et B, 285, pp. 973–975.
• Wiles, Andrew (1995). Modular elliptic curves and Fermat's last theorem, Annals of Mathematics 141 (3), 443-551 (alternative link with additional photographs).

Simon Singh Simon Lehna Singh (born 1964) is an Indian-British author of Punjabi background with a doctorate in physics from Emmanuel College, Cambridge, who has specialized in writing about mathematical and scientific topics in an accessible manner. ...

Further reading

• Aczel, Amir (hardcover, 1996). Fermat's Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem. Four Walls Eight Windows. ISBN 1-56858-077-0.
• Bell, Eric T. (1961). The Last Problem. New-York: Simon and Schuster. ISBN 0-88385-451-1 (edition of 1998).
• Benson, Donald C. (paperback, 1999). The Moment of Proof: Mathematical Epiphanies. Oxford University Press. ISBN 0-19-513919-4.
• Brudner, Harvey J. (1994). Fermat and the Missing Numbers; ISBN 0964478501
• Edwards, H. M. (1977). Fermat's Last Theorem. Springer-Verlag. ISBN 0-387-90230-9. 
• Mozzochi, Charles (2000). The Fermat Diary. ISBN 0-8218-2670-0. 
• van der Poorten, Alf (hardcover, 1996). Notes on Fermat's Last Theorem: Wiley Interscience, ISBN 0-471-06261-8. (An outline of Wiles's methods; for the mathematically sophisticated.)

Amir D. Aczel (b. ... For other persons named Eric Bell, see Eric Bell (disambiguation). ... Harvey Jerome Brudner in 2007 Harvey Jerome Brudner (born in Brooklyn, New York on May 29, 1931) is a scientist and was the Dean of Science & Technology at the New York Institute of Technology. ...

External links

• Daney, Charles (2003). The Mathematics of Fermat's Last Theorem. Retrieved Aug. 5, 2004.
• Elkies, Noam D. Tables of Fermat "near-misses" - approximate solutions of xⁿ + yⁿ = zⁿ
• Freeman, Larry (2005). Fermat's Last Theorem Blog. A blog that covers the history of Fermat's Last Theorem from Pierre Fermat to Andrew Wiles.
• Kisby, Adam William (2004). Fermat's Last Theorem Revisited: A Marginal Proof in Ten Steps (PDF). Parody.
• Ribet, Ken (1995). Galois representations and modular forms- discusses various material which is related to the proof of Fermat's Last Theorem: elliptic curves, modular forms, Galois representations and their deformations, Frey's construction, and the conjectures of Serre and of Taniyama–Shimura
• Shay, David (2003). Fermat's Last Theorem. The story, the history and the mystery. Retrieved Aug. 5, 2004.

• The bluffer's guide to Fermat's Last Theorem
• Eric W. Weisstein, Fermat's Last Theorem at MathWorld.
• Fermat's last theorem, On Sophie Germain.
• "The Proof," the title of one edition of the PBS television series NOVA, discusses Andrew Wiles effort to prove Fermat's last theorem.
• Fermat's Last Theorem by Amir D. Aczel (Chapter 1)