a simple proof of Fermat's Last Theorem

I have really found a simple proof of Fermat's Last Theorem
how can i announce this solution ?
and are there prizes on this proof ???
and where can i send that proof ??
can anyone help me ??

 

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pm me the proof, I'll see what I can do

 

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You send your work into some Math organization and then they look over it for about three years and if they see it as undoubtedly true. Your equation will be put into math books and if it's money prize problem you'll get the money.

 

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http://www.claymath.org/millennium/

If you got the idea from one of my posts. You could share the wealth

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Fermat's last theorem states that:

It is impossible to separate any power higher than the second into two like powers,
or, more precisely:

If an integer n is greater than 2, then the equation an + bn = cn has no solutions in non-zero integers a, b, and c.
In 1637 Fermat wrote, in his copy of Claude-Gaspar Bachet's translation of the famous Arithmetica of Diophantus, "I have a truly marvelous proof of this proposition which this margin is too narrow to contain." (Original Latin: "Cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet.")

Fermat's last theorem is strikingly different and much more difficult to prove than the analogous problem for n = 2, for which there are infinitely many integer solutions called Pythagorean triples (and the closely related Pythagorean theorem has many elementary proofs). The fact that the problem's statement is understandable by schoolchildren makes it all the more frustrating, and it has probably generated more incorrect proofs than any other problem in the history of mathematics. No correct proof was found for 357 years, when a proof was finally published by Andrew Wiles in 1994. The term "last theorem" resulted because all the other theorems proposed by Fermat were eventually proved or disproved, either by his own proofs or by other mathematicians, in the two centuries following their proposition.

Fermat's last theorem is one of the most famous theorems in the history of mathematics, familiar to nigh every mathematician, and had achieved a recognizable status in popular culture prior to its proof. The avalanche of media coverage generated by the resolution of Fermat's last theorem was the first of its kind, including worldwide newspaper accounts and various popularizations in books and a PBS NOVA special, The Proof.

http://math.stanford.edu/~lekheng/flt/

 

Publish it in a number theory journal: International Journal of Number Theory

Not that I know of. But you could make money from books and interviews about it.


But!
Are you sure you have a simple proof? There is a very long line of professional and amateur mathematicians who have mistakenly thought that they had proofs.

 

Some things to consider:

[Fermat's last theorem] has the dubious distinction of being the theorem with the largest number of published false proofs. For example over 1000 false proofs were published between 1908 and 1912.​

It is also worth reading these two short pages:
Zimaths: Fermat's Last Theorem
Ask NRICH: Proofs of Fermat's Last Theorem?

All over the world, university mathematics departments receive attempts to prove Fermat's Last Theorem. As the research-level mathematicians have other priorities, they do not want to spend large amounts of time corresponding with people who are very unlikely to have found a correct proof. I have heard various stories of how different departments deal with the proofs they are sent. One has a form: Dear ___, Thank you for your purported proof of Fermat's Last Theorem. The first error is on page ___ line ___. Yours sincerely, … Another files them in a central place, and if anyone's feeling bored, they might take one out and reply. I'm quite sure some departments just bin them. ​

 

this might be alittle off topic, but does anyone know if the problem of there being a atleast one prime number inbetween every 2 consecutive perfect square numbers is still an open problem (this is basically what andrica's conjecture states: http://en.wikipedia.org/wiki/Andrica's_conjecture)?

i would think that since it has been proven that there exists atleast one prime inbetween every number and that number times two, that that in and of itself would prove that there must be atleast one prime number inbetween every two consecutive square numbers, thus proving andrica's conjecture to be true.

 

yes. i read that on wikkipedia.

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http://en.wikipedia.org/wiki/Fermats_Last_Theorem#In_fiction

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oh yeah. u do realize that what may seem like "proof" to an amatuer mathamatician (i am not accusing u of being one mind you) does not meet the standards of a formal proof, correct?

i can see many reasons, besides the one's given in formal proofs, of why fermat's last theorem would be true, and they are fairly simple in my opinion, but they probably don't meet the standards of a formal proof.

 

It is known that the modern proof could not have been developed by Fermat. If he had a proof, it would be fundamentally different from the one devised by Wiles (?spelling).

If somebody actually devised another proof, I am sure he would be amply rewarded by somebody, expecially if the proof was one that might have been developed by Fermat.

 

Mathematical Logic and Fermat

Mathematical Logic and Fermat :

Using mathematical bivalent logic to establish a property inherited by coprime factors of a power of degree n equal to the sum or difference of two powers of even degree n :

Statement of property P :
P(a^n) : « The power a^n is equal to the sum or difference of two powers of even degree n ; a,n Є N+»

In the bivalent logic (excluded middle) : P(a^n) ∨ ¬P(a^n) = T ,
statement P(a^n) is true : P(a^n) = T , or false : P(a^n) = F .

Let Z = ab = ∏i m pi^αi, Z decomposed into prime factors ,
a and b are coprime, pi : prime number,
αi : integer exponent ≥ 1, i=1, 2, … , m .

Establishment of inherited property :
P(Z^n = a^n *b^n)=T => (P(a^n)=T)∨(P(b^n)=T) (1)
(reduction rule or "finite descent")

Logical propositions :
(1) :
[(∀ a,b,n Є N+ , Z=ab)
(P(Z^n = a^n *b^n)=T => (P(a^n)=T)∨(P(b^n)=T))] = T
with contrapositive :
[(∀ a,b,n Є N+ , Z=ab)
((P(a^n) = F)∧(P(b^n) = F) ==> P(Z^n = a^n * b^n) = F)]=T
restriction of :
P(Z^n = a^n *b^n)=T => (P(a^n)=T) ∧ (P(b^n)=T)
Proof :
Suppose :
(2) :
[(∃ a,b,n Є N+ , Z=ab)
(P(Z^n = a^n *b^n)=T ==> (P(a^n) = F)∧(P(b^n) = F))]

This proposition (2), contradictory of (1), has as contrapositive :
(3) :
[(∃ a,b,n Є N+ , Z=ab)
((P(a^n)=V)∨(P(b^n)=V) ==> P(Z^n = a^n * b^n)=F)] = F
Proof :
suppose b^n = x^n ± y^n, since Z^n = a^n * b^n and b^n = x^n ± y^n , we have Z^n = a^n (x^n ± y^n) and, as multiplication is distributive over addition / subtraction and associative, Z^n = a^n*x^n ± a^n*y^n = (ax)^n ± (ay)^n .
Therefore P(Zn=(ax)^n ± (ay)^n)=T contradicts the conclusion : P(Z^n = a^n * b^n) = F in the proposition (3) which is contrapositive of proposition (2), contradictory of proposition (1).
As the proposition (2), contradictory of proposition (1), leads to a contradiction, it is false and proposition (1) is true :
A - :
A1 - :
[(∀ a,b,n Є N+ , Z=ab)
(P(Z^n = a^n *b^n)=T => (P(a^n)=T)∨(P(b^n)=T))] = T
A2 - :
[(P(Z^n = a^n * b^n) = T ==> (P(a^n) = T)∨(P(b^n) = T))]
==> [(P(Zn= a^n * b^n) = T) ∧ (P(a^n) = F) ==> (P(b^n) = T)]

This proposition (A) provides an operating rule which, by successive iterations, is a reduction rule or " finite descent" under the principle of finite induction.
Therefore the proposition (A1) implies the reduction proposition :
B - :
[(P(Z^n =(∏i m pi^αi)^n) = T ==>
(P((p1^α1)^n) = T)∨(P((p2^α2)^n) = T)) ∨ .... ∨(P((pm^αm)^n) = T))] = T
with equivalent proposition :
C - : Theorem F
[(P(Z^n =(∏1 m pi^αi)^n) = T ==>
(∃pi^αi Є E={ (p1^α1) , (p2^α2) , … , (pm^αm) })(P((pi^αi)^n) = T)] = T

Let pj^αj as (P(pj^αj)^n)=T and (pj^αj)^n = y^n ±x^n ,
pj,αj,y,x are coprime , pj : prime number (even or odd)

Application :
Elementary demonstration of Fermat-Wiles’ Theorem :
( Z = ∏i m pi^αi, Z decomposed into product of prime factors ,
αi : integer exponent ≥ 1, i=1, 2, … , m)
H : [∃ Z, Y, X, n Є N+ | Z^n =Y^n +X^n]
(with Theorem F (established above) :
[(P(Z^n =(∏1 m pi^αi)^n) = T ==>
(∃ pi^αi Є E={ (p1^α1) , (p2^α2) , … , (pm^αm) })(P((pi^αi)^n) = T)] = T)
==>
C : [∃ y, x, n Є N+ |
(pi^αi)n = y^n ± x^n , pi^αi prime factor of Z, pi : even or odd , αi Є N+],
But
Theorem A :
[∀ p prime number (even or odd) and ∀ y, x, n, α Є N+ , n>2 :
(pα)^n ≠ y^n ± x^n , P((p^α)^n)=F] = T
==>
Fermat-Wiles’ theorem :
[∀ Z, Y, X , n Є N+ , n>2 : Z^n ≠Y^n+X^n , P(Z^n)=F]=T

Remarks :
I believe that it is the schema of proof announced by Pierre de Fermat (1601-1665).
Proof of theorem A :
[∀ p prime number (even or odd) and ∀ y, x, n, α Є N+ , n>2 :
(p^α)^n ≠ y^n ± x^n , P((p^α)^n)=F]=T ,
is composed in fact by two proofs of which the shortest is obvious or immediate.
(My proof of the two theorems F and A has 11 pages.)
I also believe that Abel (1802-1829) was committed to the way of the proof schema announced by Fermat (Abel‘s conjecture, 1823), but the life doesn’t give him the necessary time to find a good direction.
As for me, it is over 45 years, from time to time, I have in search of mathematical methods whose tools were known by Fermat to solve "Fermat's enigma". I tried unsuccessfully several methods (analysis, geometry, arithmetic) that don't use mathematical logic. In resuming the study of quadratic forms and Pythagorean triples, especially primitive Pythagorean triples and their generalization (Abel's conjecture), the mathematical bivalent logic appeared to me to be a lifesaving tool.
Ahmed IDRISSI BOUYAHYAOUI

© INPI-Paris

 

Don't get me started in FLT proof threads I've been involved in on NRich. If people think I get wound up here.....

 

A formal simple proof for Case 1 (n does not divide either x, y or z), has been under peer review by the International Journal of Mathematical Education in Science and Technology since early October 2009. It may take some time before results are known. Have my fingers crossed.