41. Fermat's Last Theorem A historical and biographical account. http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Fermat's_last_theorem.htm

42. Instructional Conference On Fermat's Last Theorem University of Illinois at UrbanaChampaign, USA; 618 August 2000. http://www.math.uiuc.edu/~boston/workshop.html

Note: The deadline below passed but there are still a few open spaces. If you or your student is interested, please contact us as soon as possible! Instructional Conference on Fermat's Last Theorem August 6-18, 2000 University of Illinois at Urbana-Champaign Organizing Committee: Nigel Boston UIUC Chris Skinner, IAS and Michigan From August 6-18, 2000, the Instructional Conference on Fermat's Last Theorem will be held as one of the featured events in a Special Year in Number Theory at the University of Illinois. It is intended to provide advanced graduate students with a detailed overview of the recent proof of Fermat's Last Theorem. Workshop participants will arrive Sunday, August 6 and leave at about lunchtime Friday, August 18. The meeting will consist of morning lectures by each of the organizers, followed by breaking into 4 groups of 6 students each to work on projects. These projects will fill some of the holes left in the lectures. Towards the end of the two weeks, students will present talks on their group work. There will be some social events (a reception at the start, an outing in the middle, and banquet at the end). Sponsors The conference is hosted by the Mathematics Department at the University of Illinois and is supported by the Number Theory Foundation and the National Science Foundation.

43. Richard Taylor Publications including the joint paper with Andrew Wiles which completed the proof of fermat's Last theorem. http://www.math.harvard.edu/~rtaylor/

44. UNC Charlotte Mathematics Department - What We Know About Fermat's Last Theorem A brief history. http://www.math.uncc.edu/flt.php

Chairperson: Dr. Alan Dow Associate Chairperson: Dr. Mohammad Kazemi Coordinator of Graduate Program: Dr. Joel Avrin Coordinator of Undergraduate Program: Dr. Bruno Wichnoski MathEd Coordinator: Dr. Victor Cifarelli Last updated: Back to Main Math Dept. Web Page History of Fermat's Last Theorem Pierre de Fermat (1601-1665) was a lawyer and amateur mathematician. In about 1637, he annotated his copy (now lost) of Bachet's translation of Diophantus' Arithmetika with the following statement: Cubem autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos ejusdem nominis fas est dividere: cujus rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caparet. In English, and using modern terminology, the paragraph above reads as: There are no positive integers such that x^n + y^n = z^n for n > 2 . I've found a remarkable proof of this fact, but there is not enough space in the margin [of the book] to write it. Fermat never published a proof of this statement. It became to be known as Fermat's Last Theorem (FLT) not because it was his last piece of work, but because it is the last remaining statement in the post-humous list of Fermat's works that needed to be proven or independently verified. All others have either been shown to be true or disproven long ago.

45. Karl Rubin Slides for a talk by Karl Rubin on the story of fermat's Last theorem for a general audience, including the history of the problem, the story of Andrew Wiles' solution and the excitement surrounding it, and some of the many ideas used in his proof. http://math.Stanford.EDU/~rubin/lectures/fermatslides/

46. Fermat's Theorem -- From MathWorld MathWorld Logo. Alphabetical Index. Eric's other sites. Number Theory ,Special Numbers , Figurate Numbers , Square Numbers v. fermat's theorem, http://mathworld.wolfram.com/FermatsTheorem.html

Number Theory Special Numbers Figurate Numbers Square Numbers Fermat's Theorem A prime p can be represented in an essentially unique manner in the form for integral x and y iff or p = 2. It can be restated by letting then all relatively prime solutions ( x, y ) to the problem of representing for m any integer are achieved by means of successive applications of the genus theorem and composition theorem . There is an analog of this theorem for Eisenstein integers Eisenstein Integer Square Number References Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, pp. 142-143, 1993. Author: Eric W. Weisstein Wolfram Research, Inc.

47. Fermat's Last Theorem - An Elementary Proof By Nico De Jong (1992) Edited from the book fermat's last theorem proved by Nico de Jong (1992). http://www.geocities.com/elementaryfermat

Fermat's last theorem Was Wiles' proof really first ? Edited for the Web by Nico de Jong (c)2000 The following article is an edited version of the proof in the book Fermat's last theorem proved by Nico de Jong. Pretoria : (c)1992. ISBN 0-620-16639-8 (listed in the South African National Bibliography, Pretoria State Library, 1992, 92-2617) If you would like to comment on my proof of Fermat's last theorem, e-mail me I hope you will enjoy this article and find it worthy of discussion with your friends. PREAMBLE AND ABSTRACT After 350 years of unsuccessful attempts, a mathematically highly advanced proof of Fermat's Last Theorem (FLT) by A. Wiles was accepted and published in Annals of mathematics , May 1995. However, it cannot be Fermat's own elementary demonstration. In the opinion of the present author the following proof is the one Fermat had in mind. FLT holds that the equation z w = x w + y w can have a positive integer solution if and only if w = 2. As is well known, a proof for w being any prime suffices. Therefore w is considered a prime number throughout. Suppose z is a composite positive integer. If for only one of its prime number factors, say p

48. Is Fermat's Last Theorem Proven? An attempted elementary proof of fermat's Last theorem by James Constant, rejecting that of Wiles. http://fermat.coolissues.com/wiles.htm

49. 1993: Fermat's Theorem Solved The theorem solved by Wiles was the last one and so referred to as fermat's Lasttheorem. Any mathematician will attest that, no matter how many numbers are http://www.capitalcentury.com/1993.html

Andrew Wiles flashes a huge grin after publicly showing off his proof for the first time in 1993. A shy and secretive Princeton University mathematics professor in 1993 unraveled a mystery that had frustrated and intrigued mathematicians for 350 years. Andrew Wiles, fascinated by math problems since age 10, figured out the last theorem of 17th century mathematician Pierre De Fermat, achieving what the most obsessed numbers crunchers of three centuries could not. The Scottish-born Wiles, in a rare interview, said the draw to solve the theorem, which stemmed from Fermat's studies of the ancient Greek text "Arithmetic," was so strong because the theorem was so simple-sounding. It says that while the square of a whole number can be broken into two other squares of whole numbers, the same cannot be done with cubes or higher powers. The theorem is based on the ancient equation developed by sixth century mathematician Pythagoreas, "X squared plus Y squared equals Z squared." The equation guided Pythagoreas' famous theory for calculating the hypotenuse of a triangle. Although Fermat himself claimed to have already proved the theorem, his notes were lost, and mathematicians, none of whom were able to solve it until Wiles, had often doubted the existence of a formal proof.

50. Euler's Theorem And Small Fermat's Theorem Euler's theorem and Small fermat's theorem. Finally, Euler's theoremand small fermat's theorem are proved. MML Identifier EULER_2. http://mizar.uwb.edu.pl/JFM/Vol10/euler_2.html

Journal of Formalized Mathematics Volume 10, 1998 University of Bialystok Association of Mizar Users Euler's Theorem and Small Fermat's Theorem Yoshinori Fujisawa Shinshu University, Nagano Yasushi Fuwa Shinshu University, Nagano Hidetaka Shimizu Information Technology Research Institute, of Nagano Prefecture Summary. MML Identifier: The terminology and notation used in this paper have been introduced in the following articles [ Contents (PDF format) Preliminary Finite Sequence of Naturals Modulus for Finite Sequence of Naturals Euler's Theorem and Small Fermat's Theorem Acknowledgments The authors wish to thank Professor A. Trybulec for all of his advice on this article. Bibliography 1] Grzegorz Bancerek. Cardinal numbers Journal of Formalized Mathematics 2] Grzegorz Bancerek. The fundamental properties of natural numbers Journal of Formalized Mathematics 3] Grzegorz Bancerek. Joining of decorated trees Journal of Formalized Mathematics 4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences Journal of Formalized Mathematics 5] Czeslaw Bylinski. Functions and their basic properties Journal of Formalized Mathematics 6] Czeslaw Bylinski.

51. Clare College: Guide To Subjects (Fermat's Theorem) Guide to Subjects fermat's theorem. (The article below was written for the ClareAssociation Annual in 1994. fermat's theorem is very easy to describe. http://www.clare.cam.ac.uk/admissions/subjects/fermat.html

CLARE COLLEGE Admissions Home About Clare ... Search Guide to Subjects: Fermat's Theorem (The article below was written for the Clare Association Annual in 1994. It describes, in language intended for the "intelligent layman", the history, the importance and the proof of Fermat's Theorem.) Last year saw possibly the most remarkable developments in mathematics this century - and Clare College was at the centre of it. For over 350 years mathematicians all over the world have tried without success to prove what has become known as ``Fermat's Last Theorem''. But recently a proof was announced by Andrew Wiles, using the help of Richard Taylor. A.J. Wiles (1974) was a graduate student, and then Research Fellow, in the late 1970s and is now a Professor at Princeton University; R.L. Taylor (1980), who was Wiles' research student, is currently a Fellow of Clare and Reader in Pure Mathematics. Does a n +b n =c n have a solution in integers if and Fermat's theorem is very easy to describe. Most people have come across the fact that 3 (most likely during a study of right-angled triangles). Similar examples, such as 5

52. 3.7 Time Delay And ``Fermat's'' Theorem 4 Lensing Phenomena 3 Basics of Gravitational Lensing 3.6 Lens mapping.3.7 Time delay and ``fermat's'' theorem. The deflection angle http://www.livingreviews.org/Articles/Volume1/1998-12wamb/node10.html

3.7 Time delay and ``Fermat's'' theorem The deflection angle is the gradient of an effective lensing potential (as was first shown by [ ]; see also [ ]). Hence the lens equation can be rewritten as or The term in brackets appears as well in the physical time delay function for gravitationally lensed images: This time delay surface is a function of the image geometry ( ), the gravitational potential , and the distances , and . The first part - the geometrical time delay - reflects the extra path length compared to the direct line between observer and source. The second part - the gravitational time delay - is the retardation due to gravitational potential of the lensing mass (known and confirmed as Shapiro delay in the solar system). From Equations ( ), it follows that the gravitationally lensed images appear at locations that correspond to extrema in the light travel time, which reflects Fermat's principle in gravitational-lensing optics. The (angular-diameter) distances that appear in Equation ( ) depend on the value of the Hubble constant [ ]; therefore, it is possible to determine the latter by measuring the time delay between different images and using a good model for the effective gravitational potential

53. Fermat's Last Theorem listings for exact times.) This program was originally broadcast in Britain in January1996 in the BBC Horizon series under the title fermat's Last theorem. http://www.ams.org/new-in-math/fermat.html

Fermat's Last Theorem On October 28, 1997, The Proof will be broadcast on PBS as a program in the Nova series . (See local listings for exact times.) This program was originally broadcast in Britain in January 1996 in the BBC Horizon series under the title Fermat's Last Theorem . Visit the BBC Horizon web site for information about the program, including a transcript. A review of this program is available on e-MATH. On June 23, 1993, Andrew Wiles announced to his colleagues at a mathematics conference in Cambridge, England that he had proven Fermat's Last Theorem. Email zapped around the globe as mathematicians and others celebrated the news. Newspapers all over the world trumpeted the achievement, and since then there have been many articles written about the proof. A number of web pages devoted to Fermat's Last Theorem have been started, among them the following: MacTutor History of Mathematics page on Fermat's Last Theorem University of Heidelberg page on Fermat's Last Theorem Yahoo page on Fermat's Last Theorem State University of New York at Albany Department of Mathematics gopherFermat's Last Theorem Cambridge University Department of Pure Mathematics and Mathematical Statistics gopherFermat's Last Theorem The Proof of Fermat's Last Theorem by R. Taylor and A. Wiles

54. G.Imbalzano On II Fermat'theorem & Structure Fine'constant. News 2003 for SSGRR Universe for Life ! From Holy Shroud to BigBang ! ~~~Use MS LineDraw (fixed) FONT~~~ Associazione Insegnanti http://users.libero.it/jmbalzan/newsiol.htm

: News 2003 for S.S.G.R.R. "Universe for Life" : ! From Holy Shroud to Big Bang ! ~~~Use MS LineDraw (fixed) FONT~~~ Associazione Insegnanti di Fisica: XXXV Congresso ~~~Use MS LineDraw (fixed) FONT~~~ ABSTRACT.txt ~ Riflessioni sull'Ultimo .. Fermat ~ Ricerca DIDATTICA su ://services.csi.it/~major/ #Lyricae# ~ Merci, mon ami! ~ =! Links PREFERITI != ! Antigravity Bibliography .. Very LONG ! Home Page on http://www.geocities.com/jmbalzan

55. Fermat's Theorem Using Projective Geometry Solution to fermat's theorem by CF Russell using projective geometry calculating circle Znuz is Znees vol. 4. Back to Contents. http://www.cfrussell.homestead.com/files/fermat.htm

Solution to Fermat's Theorem by C.F. Russell using projective geometry "calculating circle" - Znuz is Znees vol. 4. Back to Contents

56. Avernus - Cryptography - Fermat's Theorem fermat's theorem. If p is prime and p does not divide a, then. a p1= 1 (mod p). This is a special case of the fermat-Euler theorem. http://www.avernus.org.uk/encrypt.php?article=fermat

57. Avernus - Cryptography - Fermat-Euler Theorem where f(m) is Euler's function. This is a generalisation of fermat's theorem.See Also Euler's Function; fermat's theorem; fermat's Last theorem. Books http://www.avernus.org.uk/encrypt.php?article=fermat-euler

58. A Flaw In The Proof Of Fermat's Theorem PrevNextIndexThread A flaw in the proof of fermat's theorem. SubjectA flaw in the proof of fermat's theorem; From Mamede http://www.cis.upenn.edu/~bcpierce/types/archives/1994/msg00002.html

[Prev] [Next] [Index] [Thread] A flaw in the proof of Fermat's theorem To logic@cs.cornell.edu types@dcs.gla.ac.uk igpl@doc.imperial.ac.uk Subject : A flaw in the proof of Fermat's theorem From mamede@ime.unicamp.br Date : Sat, 15 Jan 94 03:27:49 EDT Approved : types@dcs.gla.ac.uk [This message is not strictly relevant to the Types Forum. But I am circulating it anyway, as a matter of general interest. Replies by e-mail to Mamede please. Mamede, could you please post a summary or pointer to your final article, for those of us that are interested? Philip Wadler, moderator, Types Forum] Please, whoever knows anything about A FLAW IN THE RECENT PROOF OF FERMAT'S LAST THEOREM: Please inform us! We need to write a report on the situation to a Brazilian magazine and we are looking for fresh news. Thanks a lot, Mamede Lima-Marques Center for Logic and Epistemology UNICAMP Campinas - Brazil Prev: ABSTRACT Next: BRA project `Types for Proofs and Programs' Index(es): Main Thread

59. BBC - Comedy - Fermat's Theorem Wallpaper SATURDAY 15th February 2003 Text only. Comedy, It figures,now that I'm too old to squat, they're growing like weeds! http://www.bbc.co.uk/comedy/games/wallpaper/fermat.shtml

CATEGORIES TV RADIO COMMUNICATE ... INDEX SEARCH TUESDAY 18th March 2003 Text only Two in the back, two in the front. BBC Homepage Entertainment Comedy Happiness ... Help Like this page? Send it to a friend! 640 x 480 800 x 600 1024 x 768 To download and install the desktop images, follow these instructions. Choose the size of wallpaper you require. The options are small (640 x 480); medium (800 x 400) or large (1024 x 768). Click on one of the options and a bigger image will appear in a new browser window. Move your cursor (pointer) over the big image. Right click your mouse and a 'drop down' menu will appear. Go to 'set as wallpaper'. Finally left click your mouse. Your new wallpaper will appear on your desktop. To find out the best size for you, right mouse click on your desktop, select 'properties,' a pop window will appear; select 'settings' and note the dimensions in the section called 'screen area.' Download the image by clicking and holding down the mouse. Click on the Apple icon in the top left hand corner of the screen. Go to control panels, click on 'Appearance'. Six menu items are shown - choose 'Desktop'. Click on 'Place Picture' and choose the image that you downloaded from the web site. Click 'Set Desktop' button. Sickboy' World Cup Ten Things Wav World Cyderdelic ... Privacy

60. The Converse To Fermat's Theorem The little known Converse to fermat's theorem, is the basic axiomfor all public key encryption. The Converse to fermat's theorem. http://www.newnation.ca/sniffy/fermat.html

This page uses UTF-8 to print various math symbols Return to Sniffy's Icehouse The Converse to Fermat's Theorem Off site link to details of large integer arithmeic with Perl The converse of Fermat's theorem leads to the generation of large primes that are used for electronic encryption. There is no such thing as a formula that generates prime numbers, that we know of. Only the probability that a large number is prime, can be determined, in a reasonable time. All public key encryption methods, are developed from Fermat's theorem: A p For example say that A = 3 and p = 5. For those values and obviously 240 is divisible by 5. Fermat's theorem will be true for any number A, not equal the prime number p. Now, compare Fermat's theorem with the converse of Fermat's theorem. A p if A p Ancient Chinese academics believed the second statement to be true and also assured the Emperor that he would have eternal life. The mathematicians were all exterminated, most likely on account of the Emperor's wrinkles rather than the bogus formula for generating primes. A congruence may be divided if A (or any factor) is coprime to the modulus, so that the equation may be rewritten, A p -1 Consider the number 341, and apply it to Fermat's equation using base. 2

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