21. Www.cc.gatech.edu As the press conference starts, a 10years old boy raises his hand and says that the respectable scientist has made a mistake and the Fermat theorem cannot hold for those 3 http://www.cc.gatech.edu/grads/t/tpushkar/puzzlesDownloads/minet06.rtf

22. Fermat's Little Theorem -- From Wolfram MathWorld If p is a prime number and a a natural number, then a^p=a (mod p). (1) Furthermore, if pa (p does not divide a), then there exists some smallest exponent d such that a^d1 http://mathworld.wolfram.com/FermatsLittleTheorem.html

23. Fermat's Theorem: DISPROVED 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 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.

24. PlanetMath: Euler-Fermat Theorem I am not very familiar with this area but your proof appears to assume n 0 (and a 0?) whereas the theorem statement does not? Can you clarify please? http://planetmath.org/encyclopedia/EulersTheorem.html

(more info) Math for the people, by the people. donor list find out how Encyclopedia Requests ... Advanced search Login create new user name: pass: forget your password? Main Menu sections Encyclopædia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About Euler-Fermat theorem (Theorem) If such that , then , where is the Euler totient function "Euler-Fermat theorem" is owned by full author list owner history view preamble get metadata View style: jsMath HTML HTML with images page images TeX source See Also: Fermat's little theorem Fermat's theorem proof Other names: Euler's theorem Keywords: number theory Attachments: proof of Euler-Fermat theorem (Proof) by KimJ corollary of Euler-Fermat theorem (Result) by kamala proof of Euler-Fermat theorem using Lagrange's theorem (Proof) by alozano Log in to rate this entry. view current ratings Cross-references: Euler totient function There are 6 references to this entry. This is version 6 of Euler-Fermat theorem , born on 2001-10-15, modified 2007-08-23.

25. Fermat's Last Theorem: Solving One Of The Most Perplexing Problems In Math Histo Until it was finally solved in 1993, Fermat's final theorem an extension of the Pythagorean theorem - befuddled mathematicians for more than four centuries. http://www.suite101.com/content/fermats-last-theorem-a50596

26. Fermat's Little Theorem With notes on Carmichael numbers and the life of RD Carmichael. http://www.pballew.net/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

27. Fermat Corner Fermat s Last Theorem is the most notorious problem in the but learning about Fermat s Last Theorem taught me to love mathematics for its own sake. 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.

28. Little Fermat Theorem The Little Fermat Theorem states that if p is a prime then p divides a pa, p not equal to a. After factoring a(a (p-1)-1) The converse of the theorem is not true, in fact there are http://home.earthlink.net/~usondermann/little.html

Little Fermat Theorem The Little Fermat Theorem states that if p is a prime then p divides a p -a, p not equal to a. After factoring : a(a (p-1) The converse of the theorem is not true, in fact there are composite numbers that divide a p -a. They are referred to as psuedoprimes The Fermat numbers denoted by: F n are always primes or psuedoprimes when a=2. n +1 is the suspected prime to be tested. Let a = 2 then: 2 n -2, or 2[2 n -1] is divisible by 2 n Let f = 2 n , This is a number that only has 2 as its factor. That leaves us with the expression 2 f -1 to factor. Using the fact that x -y factors to (x+y)(x-y) then 2 f -1 factors to (2 (f / 2) (f / 2) Factoring the -1 factor repeatedly until the exponent is 1 we get: f -1 factors to (2 (f / 2) (f / 4) (f / 8) (f / 16) n Example: +1 is F , or 2 +1 and 2 Substituting all values in the original expression we get 2(2 -1) is divisible by Factoring: 2 Fermat , the father of number theory, conjectured that all 2 n +1 were prime. the first four are but 2 +1 is composite. Euler proved that this number is divisible by 641. (more on all of this later) I have played with this expression trying to find a pattern to psuedoprimes . I have found that if a has the pattern of kp+1 or (kp+1) t then any number p divides the expression: a n -a.

29. Moore : The Decomposition Of Modular Systems Connected With The Doubly Generaliz The decomposition of modular systems connected with the doubly generalized Fermat theorem http://projecteuclid.org/euclid.bams/1183419221

Log in Title Author(s) Abstract Subject Keyword All Fields FullText more options Home Browse Search ... next The decomposition of modular systems connected with the doubly generalized Fermat theorem Eliakim Hastings Moore Source: Bull. Amer. Math. Soc. Volume 13, Number 6 (1907), 280-288. Related Works: Cited work: Eliakim Hastings Moore. A two-fold generalization of Fermat's theorem. Bull. Amer. Math. Soc., Volume 2, Number 7 (1896), 189199. Project Euclid: euclid.bams/1183414614 Full-text: Open access PDF File (588 KB) Links and Identifiers Permanent link to this document: http://projecteuclid.org/euclid.bams/1183419221 Mathematical Reviews number (MathSciNet): Zentralblatt MATH identifier: back to Table of Contents previous next Bulletin of the American Mathematical Society BAMS Home All Issues Search this Journal Credits ... Feeds

30. MAD Scientist: Fermat Theorem Fermat Theorem Question Fermat's Last Theorem did Fermat have proof or did he guess? Submitted 16 February, 1998 by Jerry Marcantel of Glenmora, LA USA. http://www.wwheaton.com/waw/mad/mad9.html

Fermat Theorem Question: Fermat's Last Theorem: did Fermat have proof or did he guess? Submitted 16 February, 1998 by Jerry Marcantel of Glenmora, LA USA. I am a amateur mathematician. On PBS I saw a show on the guy Andrew Wiles who proved Fermat's Last Theorem. Some of the mathematicians "hinted" that Fermat did not have any proof. That Fermat just stated his theorem with on proof. Is this a general consensus in the math community? Answer: 16 February 1998 This is definitely not my field of expertise, but I am pretty sure that it is the consensus of the experts that Fermat was probably mistaken. First, the problem has received an enormous amount of attention over the centuries from the very best mathematicians. The fact that none of them found a short proof (supposing Fermat's proof was not much longer than the margin would hold this is suggested by Fermat's description of it as "truly wonderful"), nor indeed any proof at all, makes one wonder. Second, it seems clear that if Fermat had a proof, it must have been quite different than the one we have today. For the prerequisites, the mathematical concepts used in the proof, on which Wiles was able to build, had not even been developed in Fermat's time. Third, there are some shorter partial proofs, and I think even some short, seductive, but mistaken ones, that have been discovered over the years, some by good mathematicians. Possibly Fermat's proof was one of these. Mathematicians do often guess, but of course a guess is never a proof! The inspired guess leads the way, motivates and guides the hard struggle to construct a rigorous proof, but no honest mathematician would ever knowingly say he had proved something that he had only guessed. But a strong hunch can lead you to believe a conjecture is true, and then it is not too uncommon to overlook subtle logical flaws in the proof constructed to establish the guess beyond all doubt. Wiles himself at first fell victim to such an error, which, fortunately, he was able to repair.

31. The Mathematics Of Fermat's Last Theorem Oct 29, 1997 If you have ever read about number theory you probably know that (the socalled) Fermat s Last Theorem has been one of the great unsolved http://cgd.best.vwh.net/home/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.

32. Fermat Theorem Definition Of Fermat Theorem In The Free Online Encyclopedia. Fermat's theorem ′fer‚m z ‚thir əm (mathematics) The proposition that, if p is a prime number and a is a positive integer which is not divisible by p, then a p1-1 http://encyclopedia2.thefreedictionary.com/Fermat theorem

33. A Short-Form Proof Of Fermat's Last Theorem Tom Ballard solves Fermat s Last Theorem, Puts Wiles To Shame. http://www.fermatproof.com/

Fermat's Last Theorem Proof by Tom Ballard Tom Ballard's Favorite Poem Tom Ballard's Original Notes Download FermatProof.pdf Java Triplet Generator ... Digiflux Photo Please Sign the guestbook! Read guestbook SYNOPSIS This is an improved version of an earlier treatise. It features a short-form proof that x n + y n = z n To begin, a model for squared numbers will be introduced and used to devise a method to create all Pythagorean (x + y = z ) relationships. Equations will be derived from this process which indicate the existence of a Pythagorean equation in the model for squared numbers. A model for higher powers of "n" will then be introduced. This model will be an extension of the model for squared numbers. Simple manipulations of this model will show that the "end game" packaging of quantities postulated to be x n and y n into spaces known to be x n and y n requires that x, y, and z form a Pythagorean equation ! This is totally incompatible with the postulation that x n + y n = z n FORWARD Validating Fermats assertion that he had a proof is of utmost importance. It will never be known for sure that he had a proof in his own day and age until some credible effort can be put together to substantiate this. This treatise will provide that proof.

34. PlanetMath: Corollary Of Euler-Fermat Theorem Math for the people, by the people. http://planetmath.org/encyclopedia/GeneralizationOfEulerFermatTheorem.html

(more info) Math for the people, by the people. donor list find out how Encyclopedia Requests ... Advanced search Login create new user name: pass: forget your password? Main Menu sections Encyclopædia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About corollary of Euler-Fermat theorem (Result) Corollary of Euler-Fermat theorem (F. Smarandache Let , and be the Euler totient function . Then: where $s$ and depend on $a$ and $m$ , also $s$ is one more than the number of steps in the algorithm , while is a divisor of $m$ , and they are both obtained from the following integer algorithm: Step (0): calculate the gcd of $a$ and $m$ and denote it by therefore $d_0=(a,m)$ , and also denote $m_0=m/d_0$ if go to the next step, otherwise stop; Step (1): calculate the gcd of and and denote it by therefore , and also denote if go to the next step, otherwise stop; Step (s-1): calculate the gcd of and and denote it by therefore , and also denote

35. Fermat S Little Theorem I imagine that therefore they too used the adjective little in respect of Fermat s Little Theorem. Were I lecturing on the matter I would likely declare http://www.spd.dcu.ie/johnbcos/fermat's_little_theorem.htm

36. Fermat-theorem Synonyms, Fermat-theorem Antonyms | Thesaurus.com No results found for fermattheorem Please try spelling the word differently, searching another resource, or typing a new word. Search another word or see fermat-theorem on http://thesaurus.com/browse/fermat-theorem

37. Fermat Theorem Encyclopedia Topics | Reference.com Copy paste this link to your blog or website to reference this page http://www.reference.com/browse/fermat theorem

38. Video – Myspace Video solution visualization from wolfram. fermat theorem by ok00100. Watch it on MySpace Videos. http://vids.myspace.com/index.cfm?fuseaction=vids.individual&videoid=4983923

39. A Conjecture Based On Euler Pol. And The Little Fermat Theorem little fermat theorem but the number is composite and that polynomial is known to produce a lot of primes. chances are that it will produce many primes. Even by http://sci.tech-archive.net/Archive/sci.math/2005-07/msg00396.html

a conjecture based on Euler pol. and the Little Fermat Theorem From Date : 4 Jul 2005 05:29:19 -0700 I had this idea one night a while ago, if k = n*n - n + 41 and if 2^(k-1) = 1 mod k then k is prime. It seems to work all the time, I verified for n up to 500,000,000. In other words : n*n - n + 41 is never a 2-psp, a pseudo-prime in base 2 (that is the conjecture). There is another one too : if k = n*n + 3 and if 2^(k-1) = 1 mod k then k is prime. I tried to construct an argument about the factorization of n*n - n + 41 and 2-psp's but failed to see any convincing details. I have other values that seems to work also like k = n*n + 163 (only 1 fail), another counter-example is 103*n*n - 3945*n + 34831 when n = 2400371 it does satisfy the little fermat theorem but the number is composite : 5315987*111635707. and that polynomial (103*n*n..) is known to produce a lot of primes. Based on this I launched a series of computations but (as you may know), it all comes back to the fact that the little fermat theorem produces primes very often and if we combine it with a simple g.f. like the

40. Fermat's Last Theorem (mathematics) -- Britannica Online Encyclopedia Fermat s last theorem (mathematics), the statement that there are no natural numbers (1, 2, 3, �) x, y, and z such that xn + yn = zn, in which n is a http://www.britannica.com/EBchecked/topic/204685/Fermats-last-theorem

document.write(''); Search Site: Advanced Search With all of these words With the exact phrase With any of these words Without these words Home SHOP BROWSE BLOG ... HELP Username: Password: Remember me Forgot your password? Help Email " is the e-mail address you used when you registered. Password " is case sensitive. If you need additional assistance, please contact customer support Enter the e-mail address you used when enrolling for Britannica Premium Service and we will e-mail your password to you. Fermats-last-theorem My Britannica CREATE MY Fermat's las... NEW ARTICLE ... SAVE Table of Contents: Article Article Related Articles Related Articles External Web sites External Web sites Citations Article Related Articles External Web sites Citations ARTICLE from the also called , the statement that there are no natural numbers x y , and z such that x n y n z n , in which n is a natural number greater than 2. For example, if n x y , and z exist such that x y z (i.e., the sum of two cubes is not a cube). In 1637 the French mathematician Pierre de Fermat wrote in his copy of the Arithmetica by Diophantus of Alexandria (c.

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