Re: FLT AND ITS GENERALIZATION, BEAL'S CONJECTURE

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

Date: 29 Dec 2004 11:20:24 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?

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