Geometry.Net - Theorems_And_Conjectures: Fermat Theorem

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An attempted elementary proof.
http://www.geocities.com/vala_var/
Fermat's Last Theorem -- From MathWorld
Article in Eric Weisstein's World of Mathematics.Category Science Math Diophantine Equations Fermat s Last TheoremFermat's Last Theorem, Bell, E. T. The Last Problem. New York Simon and Schuster,1961. Cipra, B. A. fermat theorem Proved. Science 239, 1373, 1988.
http://mathworld.wolfram.com/FermatsLastTheorem.html

Extractions: A theorem first proposed by Fermat in the form of a note scribbled in the margin of his copy of the ancient Greek text Arithmetica by Diophantus The scribbled note was discovered posthumously, and the original is now lost. However, a copy was preserved in a book published by Fermat's son. In the note, Fermat claimed to have discovered a proof that the Diophantine equation has no integer solutions for n The full text of Fermat's statement, written in Latin, reads "Cubum autem in duos cubos, aut quadrato-quadratum in duos quadrato-quadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet" (Nagell 1951, p. 252). In translation, "It is impossible for a cube to be the sum of two cubes, a fourth power to be the sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers. I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain." As a result of Fermat's marginal note, the proposition that the
Little Fermat Theorem
Little fermat theorem. (2)(2 10 ) n 1 is divisible by 341. X (p-1) - Y (p-1)= 0 mod(p) is another interesting fact proven by the Little fermat theorem.
http://home.earthlink.net/~usondermann/little.html

Extractions: 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.
Little Fermat Theorem
(X (p1) -1) - (Y (p-1) -1) = m, Associate and factor a (-1). p(t) - p(u) = m,Factor p via Little fermat theorem. p(tu) = pk, Substituting m=pk and Factoringp.
http://home.earthlink.net/~usondermann/little2.html

Extractions: X (p-1) - Y (p-1) = m X and Y not equal to p, a prime X (p-1) (-1) - Y (p-1) (+1) =m Subtract and Add a 1 (X (p-1) -1) - (Y (p-1) -1) = m Associate and factor a (-1) p(t) - p(u) = m Factor p via Little Fermat Theorem p(t-u) = pk Substituting m=pk and Factoring p X (p-1) - Y (p-1) = mod(p) Substituting and applying mod
The Last Fermat Theorem
The Last fermat theorem. The following paragraphs contain a shortoutlook on the Last fermat theorem with regards to Gsystems.
http://www.sweb.cz/vladimir_ladma/english/music/articles/links/gferm.htm

Extractions: Let c(s) be a number of instances in segment s. In case a^p +b^p =c^p (i.e. the Last Fermat theorem) it should hold: For example in G(p) the values c(s) are: p=2: 1, 3, 5, 7, 9, 11 13, 15, 17, 19, 21, 23, 25, 27 .. p=3: 1, 7, 19, 37, 61, 91, 127, 169, 217, 271, ... p=5: 1, 31, 211, 781, 2101, 4651, ... p=7: 1, 127, 2059, 14197, ... Only in case p=2 such sums are known: In case p=3, i.e. G(3) the values c(s) are: In the table it holds: (2a) R[i,j]=R[i,1]+R[i+1,j-1] E.g. R[3,3]=R[3,1]+R[4,2]=19+98=117 Written in an other way: (2b) R[i,j]=R[i-1,j+1]-R[i-1,1] E.g. R[4,2]=R[3,3]-R[3,1]=117-19=98 The equation (1) must hold also for every module m: Therefore, sum of numbers in a block of some adjacent rows from the first table should be equal to the numbers of one row from the second table (for each column). From the expression (b+p)^p-b^p = (mod p) and from the structure of diferential progressions of self-classes follows: s[(b+p)^p-(b+p)]/p - (b^p-b)/p = -1 (mod p ) (b+p)^p - b^p = ( mod p^2 ).
Vladimir S. Karapysh Fermat Theorem
Vladimir S. Karapysh fermat theorem Krasnodar 1997 See also VS KarapyshAMS Subject classification 00õõ Year 1997 fermat theorem
http://im.bas-net.by/mathlib/en/papers/31.html
Mbox: Wiles' Proof Of The Fermat Theorem
Wiles' proof of the fermat theorem. Zdzislaw Meglicki (Zdzislaw.Meglicki@cisr.anu.edu.au)Mon, 14 Nov 1994 160644 +1100 (EST)
http://www-unix.mcs.anl.gov/qed/mail-archive/volume-2/0077.html
Pierre De Fermat Theorem "last"
Fermat's last theorem Z sphere cu = X sphere cu + Y sphere cu (cbic units of three dimentions), sphere/cube volume ratio .367552596.
http://www.vorpublishing.com/pierre-de-fermat.html
Euler-Fermat Theorem
First of all, Fermat's theorem states that if p is a prime, then a = a p mod(p)where a is any integer If we divide by a on both sides of this equation we get
http://www.cs.usask.ca/resources/tutorials/csconcepts/encryption/Lessons/L5/Eule
Trailpost 10 More Euler Phi
Learn It. Theorem 10.1 Fermat's Theorem. 81 º 1 (mod 5). Theorem 10.2 The Euler fermat theorem. Euler proved a more powerful theorem than Fermat's Theorem.
http://www.cs.usask.ca/resources/tutorials/csconcepts/numbertheory/tutorial/trai
MAD Scientist: Fermat Theorem
fermat theorem. Question Fermat's Last Theorem did Fermat have proof or did heguess? Submitted 16 February, 1998 by Jerry Marcantel of Glenmora, LA USA.
http://spider.ipac.caltech.edu/staff/waw/mad/mad9.html

Extractions: 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? 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.
Fermat's Little Theorem
Another private reply John, In Carmichael's 1914 number theory text, he says it is often referred to as the simple fermat theorem. He also attributes
http://www.spd.dcu.ie/johnbcos/fermat's_little_theorem.htm

Extractions: Fermat's little theorem Friday 17 th August 2001 was the 400 th anniversary of the birth of Pierre de Fermat , and by way of a personal homage I decided that for the ICTMT5 meeting in Klagenfurt, Austria - held the week prior to Fermat's anniversary - I would offer a talk, using Maple, called Fermat's little theorem . It was never my intention to cover all of my prepared talk in Klagenfurt, and, in the event, I covered less than 0.1% of what I actually prepared. My Maple worksheet (129KB) may be downloaded here , and a (large) html version of it may be downloaded here large because Maple converts all outputs to gif files, and there are 447 of those in the worksheet). I dedicated my lecture to Mark Daly - a former colleague, and friend - as a token of my regard for him.
Fermat Theorem
fermat theorem. As being a amateur of mathematics, I have studiedthe fermat theorem for 20 years and gained a certain result. I
http://info.scsti.ac.cn/Ch/wwwboard/mess_busi/438.html
Re Fermat Theorem
Re fermat theorem. ? Jay Dillon on February 02, 1999 at 171744 fermat theorem ? Darong, Lan on November 18, 1998 at 201009
http://info.scsti.ac.cn/Ch/wwwboard/mess_busi/500.html
PlanetMath: Euler-Fermat Theorem
Eulerfermat theorem, (Theorem). Given , when gcd , where is the Euler totientfunction. See Also Fermat's little theorem, Fermat's theorem proof
http://planetmath.org/encyclopedia/EulerFermatTheorem.html
PlanetMath: Fermat's Theorem Proof
parent Fermat's theorem proof, (Proof). Consider the sequence . They are SeeAlso Eulerfermat theorem This object's parent. Cross-references
http://planetmath.org/encyclopedia/FermatsTheoremProof.html

Extractions: Fermat's theorem proof (Proof) Consider the sequence They are all different (modulo p) because if with then and since we get which is impossible. Now, since all these numbers are different, the set will have the possible congruence classes (although not necessarily in the same order ) and therefore and using we get
Ask Jeeves: Search Results For "Fermat Theorem"
Popular Web Sites for fermat theorem . 1. Fermat's last theorem Despite large prizesbeing offered for a solution, Fermat's Last Theorem remained unsolved.
http://webster.directhit.com/webster/search.aspx?qry=Fermat Theorem
Iatco Sergiu. Simplification Of Prove Of Fermat Theorem
Iatco Sergiu. Simplification of prove of fermat theorem. R First timeI read about Fermat's last theorem when I was 15 years old. Just
http://lib.kts.ru/TXT/fermat.txt

Extractions: R.Moldova District Rascani Village Recea itsergiu@yahoo.com Date: 4 May 1999 Dear Sir, I am an amateur mathematician. First time I read about Fermat's last theorem when I was 15 years old. Just like other people from the beginning I dreamt to prove one day it. Last year I found out that A.Wiles and R.Taylor proved it. I read this proof and I found it (just like other people) too complex. I analysed the Fermat's last theorem and I succeed to simplify it as follows: Let have Fermat's equation: a n +b n =c n , where n>2 (1) Because c=p1*...*pt, where pi - prime number, equation (1) becomes: a n +b n n *...*pt n (2) If exist such pi for which a1 n n = pi n (3) has solutions then these solutions are also solutions for (2) Let r= p1*...*pi-1*pi+1*...*pt Multiplying (3) with r n we have: (r*a1) n +(r*b1) n = pi n , let a=r*a1 b=r*b1 a n +b n n *...*pt n Theorem 1 (unproved by me) a n +b n n *...*pt
Pierre De Fermat
117648 and 117648/7=16806rest6. The general form of this strange behaviourof the numbers is called The Smaller fermat theorem .
http://www.surveyor.in-berlin.de/himmel/astro/Fermat-e.html

Extractions: Pierre de Fermat Pierre de Fermat was born at the 17th of August in 1601 in Beaumont de Lomagne, France. This birthday is not completely sure, but it is based on the fact that the christening happend at August 20. - After school he studied jurisprudence, and with an age of 30(33?) he became councillor at the court of Toulouse. According to mathematics, Fermat was amateur and probably self-tought. His sources were Greek texts about mathematics, most of all the book "Arithmetica" of Diophantos of Alexandria, covering problems of mathematics of the ancient times. Despite of his amateur state Fermat - besides of Descartes (1596-1650) - has the reputation as one of the greatest mathematician of his Century, and with Descartes he is one of the developer of the geometry of axes, and with this a founder of analytical geometry. He was one of the pioneers of infinitesimal calculation, because he was working with own methods on the integration of powers with integer and fractial exponents. With this he solved tangent problems covering the integration and differentiation of curves, the finding of maxima and zero points. He had correspondence with some famous contemporaries, besides other with Blaise Pascal and
NOVA Online | The Proof
Science show "Nova" delves into the topic of fermat's Last theorem. Find an interview with Andrew Wiles and a report on female mathematicians. of science struggled to prove what was known as fermat's Last theorem the idea that a certain simple equation had no
http://www.pbs.org/wgbh/nova/proof

Extractions: For over 350 years, some of the greatest minds of science struggled to prove what was known as Fermat's Last Theorem the idea that a certain simple equation had no solutions. Now hear from the man who spent seven years of his life cracking the problem, read the intriguing story of an 18th century woman mathematician who hid her identity in order to work on Fermat's Last Theorem, and demonstrate that a related equation, the Pythagorean Theorem, is true.

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