21. Fermat's Last Theorem Poetry Challenge Poetry by mathematicians and math fans celebrates the 1995 solution of fermat's Last theorem. Submit an entry. http://raphael.math.uic.edu/~jeremy/poetry.htm

Fermat's Last Theorem Poetry Challenge While you're here, you can check out my home page, or visit the UIC math department. A special greeting to all new visitors from the PBS home page! Check out Fermat's Last Tango , a new musical opening off broadway on November 21, 2000. The proof of Fermat's last theorem by Andrew Wiles and Richard Taylor was presented to an audience of over 300 people during a tenday conference at Boston University in August, 1995. At that conference, I issued a poetry challenge asking for occasional verse to celebrate the proof. While the authors' anonymity was preserved at the meeting, all things are revealed in time. If you would like to contribute to this poetry competition, please send your masterpiece to Jeremy Teitelbaum . The editor's decisions regarding suitability for publication in this forum are arbitrary, personal, and final. With thanks to all of the participants, here are the entries (in no particular order). Author: John Fitzgerald Fermat's last theorem Is a puzzling queer one: Squares of a plane Wholely squared, aren't arcane;

22. Fermat's Last Theorem PBS's show "Nova" interviews Andrew Wiles, the man who solved fermat's Last theorem. Read about how he did it. Wiles devoted much of his entire career to proving fermat's Last theorem, the world's most famous mathematical problem. http://www.bus.ucf.edu/lee/class/fermat.htm

Fermat's Last Theorem Who was Fermat and what was his Last Theorem? Fermat was a 17th-century mathematician who wrote a note in the margin of his book stating a particular proposition and claiming to have proved it. His proposition was about an equation which is closely related to Pythagoras' equation . Pythagoras' equation gives you: x y z You can ask, what are the whole number solutions to this equation, and you can see that: and 5 And if you go on looking then you find more and more such solutions. Fermat then considered the cubed version of this equation: x y z He raised the question: can you find solutions to the cubed equation? He claimed that there were none . In fact, he claimed that for the general family of equations: "x n y n z n where n is bigger than 2, it is impossible to find a solution. " That's Fermat's Last Theorem. Extended Fermat's Theorem? "x n y n + w n z n where n is bigger than 2, it is impossible to find a solution." No , Naom Elkies of Harvard University discovered the following counter-example in 1988. From: Simon Singh, Fermat's Enigma, Anchor Books Inc., 1997, p. 159.

23. Notes On Fermat's Last Theorem Alf van der Poorten (Wiley, 1996). Contents, reviews. http://www.maths.mq.edu.au/~alf/NotesonFLT.html

Notes on Fermat's Last Theorem Alf van der Poorten Notes on Fermat's Last Theorem Canadian Mathematical Society Series of Monographs and Advanced Texts, WileyInterscience , January, 1996 222 + xvi pages ISBN 0-471-06261-8 Library of Congress Call Number QA 244.V36 1996 An exciting introduction to number theory as reflected by the history of Fermat's Last Theorem From the US (and perhaps from anywhere) you can best order from Amazon Books , or its web equivalents. However, in Australia DA Books offers the cheapest price; it translates the US price honestly. Wiley Australia (and bookshops ordering from it) assume quite frightening prices. This book displays the unique talents of author Alfred J van der Poorten in mathematical exposition for mathematicians. Here, mathematics' most famous problem and the ideas underlying its recent solution are presented in a way that appeals to the imagination and leads the reader through related areas of mathematics. The first book to focus on Fermat's Last Theorem since Andrew Wiles presented his celebrated proof, Notes on Fermat's Last Theorem surveys 350 years of mathematical history in an amusing collection of tidbits

24. Fermat's Last Theorem Is Solved An attempted elementary proof of FLT using binomial expansions. http://www.coolissues.com/mathematics/fermat.htm

PROOF OF FERMAT'S LAST THEOREM James Constant math@coolissues.com Fermat's Last Theorem is solved using the binomial series Moved to http://fermat.coolissues.com/fermat.htm

25. Fermat's Last Theorem By Simon Singh Discusses the early and recent history of people trying to solve this perplexing problem, including Andrew Wiles' final success. Includes information about poems, limerics, the offbroadway show and a quiz. http://www.simonsingh.net/owtasite/6

26. Carmichael Numbers Test numbers for primality and pseudoprimality in Java. http://www.math.fau.edu/Richman/carm.htm

Primality testing with Fermat's little theorem If n is a prime, and b n , then b n is congruent to 1 modulo n . So if we compute b n modulo n , and don't get 1, then we can conclude that n is not a prime. n A number n is a pseudoprime to the base b if b n is congruent to 1 modulo n . If a number is a pseudoprime to a variety of bases, then it is likely to be a prime. Below you can find out which composite numbers less than m are pseudoprimes to various bases. m A Carmichael number is a composite number n such that b n is congruent to 1 modulo n for every b that is relatively prime to n . So a Carmichael number passes the Fermat's-little-theorem test as best as it can. What are the Carmichael numbers less than m m

27. Fermat's Last Theorem A historical and biographical account.Category Science Math Diophantine Equations fermat s Last theorem......fermat's last theorem. the proof is not there. To some extent, provingfermat's theorem is like climbing Everest. If a man wants to http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Fermat's_last_theorem.html

28. The Mathematics Of Fermat's Last Theorem Charles Daney's treatise on fermat's last theorem. HTML, DVI and PS. http://www.mbay.net/~cgd/flt/flt01.htm

The Mathematics of Fermat's Last Theorem Welcome to one of the most fascinating areas of mathematics. There's a fair amount of work involved in understanding even approximately how the recent proof of this theorem was done, but if you like mathematics, you should find it very rewarding. Please let me know by email how you like these pages. I'll fix any errors, of course, and try to improve anything that is too unclear. Enter Good news! Many people have asked whether the following pages of this site are available in a printable or other offline format. Apollo Hogan has generously provided TeX versions of the pages here (as of November 1997). The TeX has been processed into both DVI and PostScript forms for viewing and printing. Just select the FLT Tex Files Link to begin downloading. Another request I receive frequently is for even more detailed information about Wiles' proof. The best reference, of course, is Wiles' own paper, which can be found in the Annals of Mathematics (3), May 1995. Suffice to say, it is very difficult reading. And you'll probably find it only in a good university library.

29. Fermat, Pierre De - MacTutor, Fermat's Last Theorem History of the theorem charts its life from fermat's marginal scribblings through the hands of various math greats to the 1995 Wiles proof. fermat's last theorem. Number theory index http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Fermat%27s_last_theorem.h

30. Fermat fermat is best remembered for this work in number theory, in particularfor fermat's Last theorem. This theorem states that. x n + y n = z n. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Fermat.html

31. The Mathematics Of Fermat's Last Theorem The Mathematics of fermat's Last theorem. Welcome to one of the mostfascinating areas of mathematics. There's a fair amount of work http://cgd.best.vwh.net/home/flt/flt01.htm

The Mathematics of Fermat's Last Theorem Welcome to one of the most fascinating areas of mathematics. There's a fair amount of work involved in understanding even approximately how the recent proof of this theorem was done, but if you like mathematics, you should find it very rewarding. Please let me know by email how you like these pages. I'll fix any errors, of course, and try to improve anything that is too unclear. Enter Good news! Many people have asked whether the following pages of this site are available in a printable or other offline format. Apollo Hogan has generously provided TeX versions of the pages here (as of November 1997). The TeX has been processed into both DVI and PostScript forms for viewing and printing. Just select the FLT Tex Files Link to begin downloading. Another request I receive frequently is for even more detailed information about Wiles' proof. The best reference, of course, is Wiles' own paper, which can be found in the Annals of Mathematics (3), May 1995. Suffice to say, it is very difficult reading. And you'll probably find it only in a good university library. So, I will suggest some recent books which provide more background. If you follow the links, you will be able to purchase the books online.

32. Fermat's Little Theorem With notes on Carmichael numbers and the life of R.D. Carmichael. http://www.geocities.com/Paris/Rue/1861/FermLit.html

Fermat's Little Theorem   The famous "Last Theorem" for which Fermat is best know by students is not used nearly so often as the one which is remembered as his "little" theorem.  The little theorem is often used in number theory in the testing of large primes and simply states that:  if p is a prime which does not divide a, then a p-1 =1 (mod p) .  In more simple language this says that if p is a prime that is not a factor of a, then when a is multiplied together p-1 times, and the result divided by p, we get a remainder of one.  For example,  if we use a=7 and p=3, the rule says that 7 divided by 3 will have a remainder of one.  In fact 49/3 does have a remainder of one. The theorem was first stated by Fermat in a letter in 1640 without a proof. Euler gave the first published proof in 1736. Here is a link to a proof of the theorem    The theorem is a one direction theorem, what mathematicians call "necessary, but not sufficient".  What that means is that although it is true for all primes, it is not true JUST for primes, and will sometimes be true for other numbers as well.  For example 3

33. The Mathematics Of Fermat's Last Theorem The Mathematics of fermat's Last theorem Welcome to one of the most fascinating areas of mathematics. http://www.best.com/~cgd/home/flt/flt01.htm

The Mathematics of Fermat's Last Theorem Welcome to one of the most fascinating areas of mathematics. There's a fair amount of work involved in understanding even approximately how the recent proof of this theorem was done, but if you like mathematics, you should find it very rewarding. Please let me know by email how you like these pages. I'll fix any errors, of course, and try to improve anything that is too unclear. Enter Good news! Many people have asked whether the following pages of this site are available in a printable or other offline format. Apollo Hogan has generously provided TeX versions of the pages here (as of November 1997). The TeX has been processed into both DVI and PostScript forms for viewing and printing. Just select the FLT Tex Files Link to begin downloading. Another request I receive frequently is for even more detailed information about Wiles' proof. The best reference, of course, is Wiles' own paper, which can be found in the Annals of Mathematics (3), May 1995. Suffice to say, it is very difficult reading. And you'll probably find it only in a good university library. So, I will suggest some recent books which provide more background. If you follow the links, you will be able to purchase the books online.

34. NOVA Online | The Proof | Solving Fermat: Andrew Wiles I was just browsing through the section of math books and I found this one book,which was all about one particular problem fermat's Last theorem. http://www.pbs.org/wgbh/nova/proof/wiles.html

Solving Fermat: Andrew Wiles Andrew Wiles devoted much of his entire career to proving Fermat's Last Theorem, the world's most famous mathematical problem. In 1993, he made front-page headlines when he announced a proof of the problem, but this was not the end of the story; an error in his calculation jeopardized his life's work. Andrew Wiles spoke to NOVA and described how he came to terms with the mistake, and eventually went on to achieve his life's ambition. NOVA: Many great scientific discoveries are the result of obsession, but in your case that obsession has held you since you were a child. ANDREW WILES: I grew up in Cambridge in England, and my love of mathematics dates from those early childhood days. I loved doing problems in school. I'd take them home and make up new ones of my own. But the best problem I ever found, I found in my local public library. I was just browsing through the section of math books and I found this one book, which was all about one particular problem Fermat's Last Theorem. This problem had been unsolved by mathematicians for 300 years. It looked so simple, and yet all the great mathematicians in history couldn't solve it. Here was a problem, that I, a ten year old, could understand and I knew from that moment that I would never let it go. I had to solve it. NOVA: Who was Fermat and what was his Last Theorem?

35. CATHOLIC ENCYCLOPEDIA: Augustin-Louis Cauchy (Catholic Encyclopedia) Theory of polyhedra, symmetrical functions, proof of a theorem of fermat which had baffled mathematicians like Gauss and Euler. http://www.newadvent.org/cathen/03457a.htm

Home Encyclopedia Summa Fathers ... C > Augustin-Louis Cauchy A B C D ... Z Augustin-Louis Cauchy Napoleon at Cherbourg. While here he devoted his leisure moments to mathematics. Several important memoirs from his pen, among them those relating to the theory of polyhedra, symmetrical functions, and particularly his proof of a theorem of Fermat which had baffled mathematicians like Gauss and Euler, made him known to the scientific world and won him admittance into the Academy of Sciences. At about the same time the Grand Prix offered by the Academy was bestowed on him for his essays on the propagation of waves. After a sojourn of three years at Cherbourg his health began to fail, and he resigned his post to begin at the age of twenty-two his career of professor at the Ecole Polytechnique. In 1818 he married Mlle. de Bure, who, with two daughters, survived him. Napoleon III in the cases of Cauchy and Arago, and he was thus free to continue his lectures. He spent the last years of his life at Sceaux, outside of Paris, devoting himself to his mathematical researches until the end. Society of Jesus VALSON

36. Math Forum: Ask Dr. Math FAQ: Fermat's Last Theorem is very indirect, and involves two branches of mathematics which at face value appearto have nothing to do either with each other or with fermat's theorem. http://mathforum.org/dr.math/faq/faq.fermat.html

Ask Dr. Math: FAQ F ermat's L ast T heorem Dr. Math FAQ Classic Problems Formulas Search Dr. Math ... Dr. Math Home What is the current status of Fermat's Last Theorem? In the margin of his copy of a book by Diophantus, Pierre de Fermat wrote that it is possible to have a square be the sum of two squares, but that a cube can not be the sum of two cubes, nor a fourth power be a sum of two fourth powers, and so on. Further, he wrote that he had found a truly marvelous proof which the margin was too small to contain. Fermat's Last Theorem states that x n + y n = z n That is to say, there are no integers x, y, z such that x + y = z , or integers x, y, z such that x + y = z Although this is easily stated, it has proved to be one of the most puzzling problems in the whole history of mathematics. Long after all the other statements made by Fermat had been either proved or disproved, this remained; hence it is called Fermat's Last Theorem (actually, Conjecture would be more accurate than Theorem). This conjecture was worked on by many famous mathematicians. Fermat himself proved this theorem for n = 4, and Leonhard Euler did n = 3. Special cases were dispatched one after another. New theories were developed to attack the problem, but all attempts at a general proof failed. They failed, that is, until this decade, when, building on work of many famous mathematicians, Prof. Andrew Wiles of Princeton University finally proved it. His method could not have been known to Fermat. Fermat's "truly marvelous proof" is now believed to have been faulty.

37. TV STUDIO Videos For Sale - L.M.S Video of a popular lecture on FLT arranged by the London Mathematical Society. http://www.lib.ic.ac.uk/av/vids_lms.html#A1.14

London Mathematical Society - 'Popular Lecture Series' Games Animals Play. Professor J.Maynard Smith Game theory is applied by an eminent biologist to give an insight into animal contests (for instance, for mates), leading to an explanation of why there are an (almost) equal number of male and female births, the behaviour of the Hamadryas Baboon, and the funnel web spider. Prerequisites: none, but a knowledge of pay-off matrix would be helpful and some idea of evolution. prod# 1106 - dur 38'06" - year of production July 1986. Order details The Rise and Fall of Matrices. Professor W.Ledermann. A description of the revolutionary paper of 1858 by Cayley and the change of emphasis of the teaching of linear algebra from determinants to matrices and linear maps, with historical background. Prerequisites: Some knowledge of Matrices. prod# 1107 - dur 42'48" - year of production July 1986. Order details Games That Solve Problems Professor W.A.Hodges. Mathematicians don't just solve problems. They also find methods for solving new kinds of problems. How can they do this? The lecture describes various attempts to answer this question during the last 150 years. One important recent approach is based on a kind of 'spot the difference' game; simple examples are given. Prerequisites: an interest in abstract ideas and patterns.

38. About "Il Fermat' Theorem" Translate this page Il fermat' theorem. Library Home Full Table of Contents Suggesta Link Library Help Visit this site http//www.geocities http://mathforum.org/library/view/6501.html

Il Fermat' Theorem Library Home Full Table of Contents Suggest a Link Library Help Visit this site: http://www.geocities.com/CapeCanaveral/1924/mathema.htm Author: G. Imbalzano Description: Levels: College Research Languages: Italian Resource Types: Articles Math Topics: History and Biography Number Theory Suggestion Box Home ... Search http://mathforum.org/ webmaster@mathforum.org

39. Fermat's Theorem: DISPROVED fermat's Last theorem Disproved by I. Savant of Marietta, Georgia. Innovativethinking led least an Emmy. fermat's theorem DISPROVED. http://home.mindspring.com/~jbshand/ferm.html

FERMAT's Last Theorem Disproved by I. Savant of Marietta, Georgia. Innovative thinking led to the discovery of solutions to the infamous equation that has baffled mathematicians for a decade. Savant has already become a semi-celebrity, and is the odds on favorite as next years Nobel Prize winner, or at least an Emmy Fermat's Theorem: DISPROVED (IP-Atlanta) The Mathematics community was stunned early yesterday after one of the all-time greatest mysteries was resurrected and then finally put to rest by a Marietta Georgia man. I.Savant, a reclusive bachelor who some say might be related to Elvis or Phyllis Diller, announced that he had discovered several solutions to the what some have called the Holy Grail of Mathematics: Fermat's Last Theorem The theorem is deceiving in its simplicity. Thousands of weeks ago, it was born when the famous mathematician Fermat scribbled a cryptic note in the margin of a journal. The note said that he had stumbled upon a marvelous proof of the following: Unfortunately, as legend has it, Fermat never actually put the proof on paper, and it was lost forever. Every great mathematical mind since has attempted to prove the theorem, and some even claimed success. But Mr. Savant thinks that Fermat knew it would never be proven. Says Mr. Savant: I think Fermat succumbed to pressure when he claimed that he had found a proof, and I don't blame him. I mean, there's this theorem named after you, and they even tell you that it's the last one you're getting. Hell yeah, you're going to tell them you proved it. For years people have tried to show that Fermat's Last Theorem is true. Some have tried to show it was not untrue, and others have tried to show that it was not-not-not unfalse. It dawned upon me that no one had really tried to show that it was un-not not-not-anti-not untrue. When I looked at it this way, I immediately found that it was what I just said it was, and at that point I knew I had stumbled upon a great discovery.

40. G.Imbalzano On II Fermat'theorem. 1988 II fermat' theorem and GENERALIZATION for Imbalzano! ~~~ Use MS LineDrawFONT; II fermat' theorem.. ASC~~~; fermat'88 The author ..  http://www.geocities.com/CapeCanaveral/1924/mathema.htm

1988: II Fermat' Theorem and GENERALIZATION for Imbalzano! ~~~ [Use MS LineDraw FONT] II Fermat' Theorem.. [ASC]~~~ Fermat'88: The author .. 1988..II Theorem ' * * * * * * * * * * * ' Decade..1998 ' TRUE first PROOF and GENERALIZATION ' (C) Giovanni Imbalzano for Pierre de Fermat : * (C) FERMATgi.DOC (C) * (Cfr. ISSN: 1120-6527 La Fisica nella Scuola XXXI n°1 Suppl. A.I.F. 1998) Come back..?

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