41. The Prime Glossary: Fermat's Little Theorem numbers. This pages contains the entry titled fermat s little theorem. Come explore a new prime term today! fermat s Little theorem. Let http://primes.utm.edu/glossary/page.php?sort=FermatsLittleTheorem

42. 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/

43. Crank Dot Net | Fermat's Last Theorem fermat s Last theorem Proved and Award Offered for Refutation 2002 May 13 fermat s Last theorem fermat s theorem Disproved 2000 Jul 02 http://www.crank.net/fermat.html

In Defense of Mr. Fermat 2002 May 13 Fermat's Last Theorem "During the course of studies on the Goldbach Conjecture, using finite methods, what seems to be an elementary proof of Fermat's 'Last' Theorem has been found. Astonishing here is the lucidity of the arguments and immediacy of their logic. Hopefully, by (numeric) application to the so-called 'hard' problems of Number Theory, some manner of agreement (disputation) will arise." Fermat's Last Theorem Proved and Award Offered for Refutation 2002 May 13 Fermat's Last Theorem "Here we will look at another method of simple proof of Fermat's Last Theorem (FLT) which was published in the booklet 'Fermat's Last Theorem Proved and Award Offered for Refutation' in 1990 with a supplement in 1994 which discussed many invalid but interesting criticisms. (This page will be available on the Internet for interest of mathematicians in seeing the proof, however for the Award conditions ( award valid till the end of 2003) and full discussion of criticisms readers are requested to Purchase the book.)" A Search For Fermat's Lost Proof 2002 Jan 21 Fermat's Last Theorem "This is an initial search for the undiscovered proof of Fermat. ... Stay tuned."

44. Fermat Corner 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, limericks, the offBroadway show and a quiz. http://www.simonsingh.net/Fermat_Corner.html

Fermat Corner Back to Homepage The Whole Story Who was Fermat? What is the Theorem? ... Wolfskehl Prize Andrew Wiles Fermat Corner Fermat’s Last Theorem is the most notorious problem in the history of mathematics and surrounding it is one of the greatest stories imaginable. This section explains what the theorem is, who invented it and who eventually proved it . When finished, it will also tell the fascinating stories of the some of the other mathematicians whose lives were tormented by this beautiful and intriguing problem. Fermat’s Last Theorem dominated my own life for four years, because I made a TV documentary, wrote a book and then lectured on the subject. Getting involved in Fermat’s mischievous conundrum set me on the path towards being an author and ignited an interest in mathematics that has continued ever since. As a physicist, I was always interested in mathematics as a tool for studying the universe, but learning about Fermat’s Last Theorem taught me to love mathematics for its own sake. There is a Mathematics Corner currently being developed for this site.

45. 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

46. 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

47. LookSmart - Directory - Fermat's Last Theorem fermat s Last theorem Find guides to the history of fermat s lasttheorem, or read about the men who solved and failed to solve it. http://search.looksmart.com/p/browse/us1/us317914/us328800/us1164188/us10022111/

@import url(/css/us/style.css); @import url(/css/us/searchResult1.css); Home IN the directory this category YOU ARE HERE Home Sciences Mathematics Number Theory Fermat's Last Theorem - Find guides to the history of Fermat's last theorem, or read about the men who solved and failed to solve it. Directory Categories Guides Wiles, Andrew Beal, Andrew Consolation Prizes Directory Listings About 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, Pierre de - Math of Fermat's Last Theorem Extensive site explains and demonstrates the mathematics behind the proof of Fermat's last theorem. Follow links to other last theorem sites. Fermat, Pierre de - Mathematics of the Last Theorem Details the controversy surrounding Fermat's Last Theorem, describes the math that's involved, and offers a proof. Follow links to other sites. Fermat, Pierre de - Prometheus Lengthy and detailed history explains why Fermat's theorem has been so hard to prove and charts many of the attempts, including Andrew Wiles'. We're always looking for ways to improve your search experience.

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/fermat.htm

49. Fermat's Theorem - Encyclopedia Article About Fermat's Theorem. Free Access, No encyclopedia article about fermat s theorem. fermat s theorem in Free onlineEnglish dictionary, thesaurus and encyclopedia. fermat s theorem. http://encyclopedia.thefreedictionary.com/Fermat's theorem

Dictionaries: General Computing Medical Legal Encyclopedia Fermat's theorem Word: Word Starts with Ends with Definition The 17th century (16th century - 17th century - 18th century - more centuries) As a means of recording the passage of time, the 17th Century was that century which lasted from 1601-1700. During this period, the power of England and the United Provinces increased; while that of Spain and Portugal declined. Events Major changes in philosophy and science take place, often characterised as the Scientific revolution. Click the link for more information. mathematician Pierre de Fermat Pierre de Fermat (August 17, 1601 - January 12, 1665) was a French lawyer and amateur mathematician who is generally given minor credit for the development of modern calculus; in particular, for his work regarding tangents and stationary points. His work was such that he is sometimes regarded as the "father" of, both, differential calculus and number theory. He also made notable contributions to analytic geometry and probability. Click the link for more information.

50. Proof Disproved for the same reasons fermat's Last theorem is proved by a binomial infinite series expansion http://www.coolissues.com/mathematics/Beal/beal.htm

BEAL'S CONJECTURE DISPROVED James Constant math@coolissues.com Beal's Conjecture is disproved for the same reasons Fermat's Last Theorem is proved. Beal's conjecture A prize is offered for proof or disproof of Beal's conjecture , stated as follows: If x,y,z,m,a,b positive integers then x,y,z have a common factor Proof of Fermat's Last Theorem A proof of Fermat's Last Theorem (FLT) is available using the binomial expansion . In this proof it is shown that z cannot be an integer in the equality x,y,z,m positive integers thus proving FLT x,y,z,m positive integers Disproof of Beal's Conjecture When a=b=m , Beal's equation (1) becomes Fermat's equation (2). Clearly, Fermat's equation (2) is a special case of Beal's equation (1). The same procedure used in Fermat's equation (2) can be used to show that z cannot be an integer in Beal's equation (1). Start by rearranging Beal's equation (1) x,y,z,m positive integers and then expressing the parenthesis term as a binomial series, with results 1. Since m 1/m is not an integer and the series cannot terminate becoming the binomial theorem.

51. Fermat-Euler Theorem - Encyclopedia Article About Fermat-Euler Theorem. Free Acc encyclopedia article about fermatEuler theorem. fermat-Euler theorem in Freeonline English dictionary, thesaurus and encyclopedia. fermat-Euler theorem. http://encyclopedia.thefreedictionary.com/Fermat-Euler theorem

Dictionaries: General Computing Medical Legal Encyclopedia Fermat-Euler theorem Word: Word Starts with Ends with Definition In number theory Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers and contains many open problems that are easily understood even by non-mathematicians. More generally, the field has come to be concerned with a wider class of problems that arose naturally from the study of integers. Number theory may be subdivided into several fields according to the methods used and the questions investigated. See for example the list of number theory topics. Click the link for more information. Euler's theorem (also known as the Fermat-Euler theorem ) states that if n is a positive integer The integers consist of the natural numbers (0, 1, 2, ...) and their negatives (-1, -2, -3, ...; -0 is equal to and therefore not included as a separate integer). The set of all integers is usually denoted in mathematics by Z (or Z in blackboard bold, ), which stands for Zahlen (German for "numbers"). They are also known as the

52. On The Beal Conjecture An elementary proof of Beal's Conjecture given the proof of fermat's Last theorem. http://geocities.com/kerrymerry2000/

Sign Guestbook View Guestbook View Page Stats The Full Beal Conjecture The primary reference source for this proof is, “In Defense of Mr. Fermat.” It may be downloaded from nearly any search directory. The paper is necessary to follow the accompanied discussion. The object is to show that: b r + a n = p q is impossible when the exponents, r, n, and q, are positive and greater than 2 and a,b and p are coprime. Consider the following which is always solvable for “a” and “b.” a + b = p q a and b can now be defined in terms of each other under the transformation, T:, when r, n, and q are at least 3 making the transformation definitive (reversible) T: [a b r , b a n ] , such that: T: (a+b) = a n + b r = p q This transformation may be applied any number of times as long as it remains consistent: T: (a n + b r ) = a rn + b rn = p q Should this latter transformation hold, it is somewhat trivial to say that a rn and b rn may be represented by the simple sum, x + y. Originally, p q was expressed as a + b so that now a and b can be redefined as x snd y to determine a new solution that satisfies (x n + y r = p q under the transformation. However, the fact remains that (b

53. The Mathematics Of Fermat's Last Theorem That, then, is a very brief overview of the mathematical cast of characterswhich play leading roles in the eventual resolution of fermat s theorem. http://www.mbay.net/~cgd/flt/fltmain.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. Introduction If you have ever read about number theory you probably know that (the so-called) Fermat's Last Theorem has been one of the great unsolved problems of the field for three hundred and fifty years. You may also know that a solution of the problem was claimed very recently - in 1993. And, after a few tense months of trying to overcome a difficulty that was noticed in the original proof, experts in the field now believe that the problem really is solved. In this report, we're going to present an overview of some of the mathematics that has either been developed over the years to try to solve the problem (directly or indirectly) or else which has been found to be relevant. The emphasis here will be on the "big picture" rather than technical details. (Of course, until you begin to see the big picture, many things may look like just technical details.) We will see that this encompasses an astonishingly large part of the whole of "pure" mathematics. In some sense, this demonstrates just how "unified" as a science mathematics really is. And this fact, rather than any intrinsic utility of a solution to the problem itself, is why so many mathematicians have worked on it over the years and have treated it as such an important problem.

54. 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.

55. Did Fermat Prove This Theorem? next up previous contents Next Prime Numbers Up fermat s Last theorem PreviousRelated Conjectures. Did fermat prove this theorem? No he did not. http://db.uwaterloo.ca/~alopez-o/math-faq/node26.html

Next: Prime Numbers Up: Fermat's Last Theorem Previous: Related Conjectures Did Fermat prove this theorem? No he did not. Fermat claimed to have found a proof of the theorem at an early stage in his career. Much later he spent time and effort proving the cases n =4 and n =5. Had he had a proof to his theorem earlier, there would have been no need for him to study specific cases. Fermat may have had one of the following ``proofs'' in mind when he wrote his famous comment. Fermat discovered and applied the method of infinite descent, which, in particular can be used to prove FLT for n =4. This method can actually be used to prove a stronger statement than FLT for n =4, viz, has no non-trivial integer solutions. It is possible and even likely that he had an incorrect proof of FLT using this method when he wrote the famous ``theorem''. He had a wrong proof in mind. The following proof, proposed first by Lame' was thought to be correct, until Liouville pointed out the flaw, and by Kummer which latter became and expert in the field. It is based on the incorrect assumption that prime decomposition is unique in all domains.

56. Fermat's Last Theorem fermat s Last theorem. History of fermat s Last theorem; What is the currentstatus of FLT? Related Conjectures; Did fermat prove this theorem? http://db.uwaterloo.ca/~alopez-o/math-faq/node22.html

Next: History of Fermat's Last Up: Number Theory Previous: Number Theory Fermat's Last Theorem History of Fermat's Last Theorem What is the current status of FLT? Related Conjectures Did Fermat prove this theorem? Alex Lopez-Ortiz Mon Feb 23 16:26:48 EST 1998

57. FermatsLittleTheorem fermat s little theorem (English). Search for fermat s little theorem in NRICH PLUS maths.org Google. Definition level 2. http://thesaurus.maths.org/dictionary/map/word/709

Home Preferences Help User Guides ... Forum thesaurus.maths.org alphabetical galleries topics For Quick Reference: drag this m-button to your links toolbar Find word or phrase containing matching starting with ending with in English English Danish German Spanish ... Slovak Fermat's little theorem (English) Search for " Fermat's little theorem " in NRICH PLUS maths.org Google Definition level 2 If p is a prime, and a is an integer that is not a multiple of p, then Definition level 4 a mod p). Equivalently, a p Show graph Requires Java Relations broader: (en) Euler's theorem (en) Theorem Funded by: EU Socrates Minerva, HeyMath!, Cambridge University Press

58. FermatsLastTheorem fermat s last theorem (English). Search for fermat s last theorem in NRICH PLUS maths.org Google. Definition level 2. If http://thesaurus.maths.org/mmkb/entry.html?action=entryById&id=642

59. Fermat's Last Theorem That s fermat s Last theorem. Extended fermat s theorem? x To someextent, proving fermat s theorem is like climbing Everest. If http://www.cba.ua.edu/~jlee/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.

60. Euler Function And Theorem The proof is completely analogous to that of the fermat s theorem except that insteadof the set of nonnegative remainders {1,2, ,m-1} we now consider the http://www.cut-the-knot.org/blue/Euler.shtml

CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site Euler Function and Theorem Euler's generalization of the Fermat's Little Theorem depends on a function which indeed was invented by Euler (1707-1783) but named by J.J.Sylvester (1814-1897) in 1883. I never saw an authoritative explanation for the name totient he has given the function. In Sylvestor's opinion mathematics is essentially about seeing "differences in similarity, similarity in difference." The word totient rhymes with quotient and the function has to do with division but in an unusual way. (Scott Brodie brougt to my attention that the Oxford English Dictionary brings up the latin root tot for adding up, total. Tot has also the meaning (of unkown origin) of a small child or a small drink. It would be very much in the spirit of the above maxim to use the word with two so different meanings. You could expect this from Sylvester whom E.T. Bell has christened hothead.) The Euler's totient function for integer m is defined as the number of positive integers not greater than and coprime to m. A few first values: (13)=12, etc., do not appear to follow any law. But there is a formula discovered by Euler to which we shall turn shortly. In one special case the formula is really simple: for prime p

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