Re: FLT AND ITS GENERALIZATION, BEAL'S CONJECTURE

From: S. Enterprize Company (smart1234_at_aol.com)
Date: 12/29/04 

Date: 29 Dec 2004 12:29:01 GMT

>>Nick Ancuta-Nazari wrote:
>>> I kindly ask those interested in this subject to comment on my
>>> approach "FLT AND ITS GENERALIZATION".
>>> Thank you very much.
>>> Regards,
>>> Nick Ancuta-Nazari
>>> nanazari@prodigy.net
>>>
>>> The TeX file is at
>>>
>>http://www.meadowdance.org/Wordsworth/Deliverables/FLT&BealConjecture.tex
>>>
>>> The PDF file is at
>>>
>>http://www.meadowdance.org/Wordsworth/Deliverables/FLT&BealConjecture.pdf
>>
>>The links about this conjecture, flt and its generalization no longer
>>work, but info about Beal Conjecture is available at
>>
>>http://www.ams.org/new-in-math/mathnews/beal.html
>>
>>> As a banker in Dallas, Texas, Andrew Beal has an obvious
>>> interest in numbers. But he has another interest that is not so
>>> obvious: He is interested in the mathematical theory of numbers.
>>> An amateur mathematics enthusiast, Beal came upon a question in
>>> number theory that even the experts can't answer. The question turns
>>> out to be at the frontier of research in the field, with connections
>>> to other deep mysteries in mathematics. To spur mathematicians to
>>> solve the problem, Beal has offered a prize of $5,000 for its
>>> solution.
>>> The prize will increase by $5,000 every year up to the amount of
>>> $50,000.
>>> Will the Beal Prize Problem become the next Fermat's Last
>>> Theorem? Indeed, it is a generalization of that famous old problem,
>>> which Pierre de Fermat proposed over 300 years ago. Like the
>>> Fermat problem, the Beal Conjecture is easily stated:
>>> If A^x + B^y = C^z,
>>> then A, B, and C have a common factor. (Here all the letters
>>> represent whole numbers, with x, y, and z bigger than 2. Two
>>> numbers have a "common factor" if there is a number that divides
>>> both of them evenly. For example, 12 and 63 have a common factor
>>> of 3.)
>>> Another resemblance between the Beal Conjecture and Fermat's Last
>>> Theorem is that both had prizes established for their solutions. In
>>> 1996, after Andrew Wiles made international headlines by presenting
>>> the number theory arsenal that finally brought down Fermat's Last
>>> Theorem, he collected the Wolfskehl Prize. Established in 1908 with
>>> funds from the will of a German physician and amateur
>>> mathematician, Paul Wolfskehl, the Wolfskehl Prize enormously
>>> increased the fame of Fermat's Last Theorem by drawing thousands
>>> of entries from all over the globe.
>>> The article, "A Generalization of Fermat's Last Theorem: The
>>> Beal Conjecture and Prize Problem," by Professor Daniel Mauldin,
>>> appears in the December 1997 issue of the Notices of the AMS. This
>>> article provides further details about Beal's question and its role
>>> in modern number theory. See also the web site
>>> http://www.math.unt.edu/~mauldin/beal.html.
>>and the latest information at
>>http://www.math.unt.edu/~mauldin/beal.html
>>> THE BEAL CONJECTURE AND PRIZE
>>> BEAL'S CONJECTURE: If A^x +B^y = C^z ,
>>> where A, B, C, x, y and z are
>>> positive integers and x, y and z are all greater than 2,
>>> then A, B and C
>>> must have a common prime factor.
>>> THE BEAL PRIZE. The conjecture and prize was announced in the
>>> December 1997 issue of the Notices of the American Mathematical
>>> Society. Since that time Andy Beal has increased the amount of the
>>> prize for his conjecture.
>>> The prize is now this: $100,000 for either a
>>> proof or a counterexample of his conjecture. The prize money is being
>>> held by the American Mathematical Society until it is awarded. In the
>>> meantime the interest is being used to fund some AMS activities and
>>> the annual Erdos Memorial Lecture.
>>> CONDITIONS FOR WINNING THE PRIZE. The prize will be
>>> awarded by the prize committee appointed by the American
>>> Mathematical Society. The present committee members are Charles
>>> Fefferman, Ron Graham, and Dan Mauldin. The requirements for the
>>> award are that in the judgment of the committee,
>>> the solution has been
>>> recognized by the mathematics community. This includes that either a
>>> proof has been given and the result has appeared in a reputable
>>> refereed journal or a counterexample has been given and verified.
>>> PRELIMINARY RESULTS. If you have believe you have solved the
>>> problem, please submit the solution to a reputable refereed journal.
>>> If you have questions, they can be mailed to:
>>> The Beal Conjecture and Prize
>>> c/o Professor R. Daniel Mauldin
>>> Department of Mathematics
>>> Box 311430
>>> University of North Texas
>>> Denton, Texas 76203
>>
>>> Questions and queries can also be FAXED to 940-565-4805 or sent by
>>> e-mail to
>>> mauldin@unt.edu
>>> LINKS TO ARTICLES ABOUT THE CONJECTURE AND PRIZE
>>
>>> The Beal Conjecture
>>> Notices American Mathematical Society, December 1997
>>> Manchester Guardian January 8, 1998
>>> A computer study has been carried out by Peter Norvig who is Chief of
>>> the Computational Sciences Division at the NASA Ames Research
>>> Center. The program and results may be found at
>>> Beal's Conjecture: A Search for Counterexamples
>>
>
>
> I tried and I think the close as you can get to equality of both sides of
>the equation is:
>
>7^3 ~= 6^3 + 5^3
>
>343 ~= 341
>
> Almost any other number combination has a larger difference.
>
> Would this qualify as a counter-example proof or proof?
>

  You know I think that I can disprove, Fermat's Last Theorem.

The basic form is established,

a^n + b^n = c^n
n >2
a,b,c are integers

Let m = 7^3 = 343 <-- the left hand side of equation
Let n = 6^3 + 5^3 = 341 < -- the right hand side of equation
     
 7^3 = 6^3 + 5^3
 434 = 341

(m + n)/2 = 342

The average difference on each side of the equation is equal to 342.

  Using Surreal Non-standard Analysis,

  { 341 | 343 } = 342

   Equality IS found at the cut location.

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