TIA,
On Tue, 25 Nov 1997, Phil Mahler wrote:
> The November 28 1997 edition of The Chronicle of Higher Education has an
> article about a banker who discovered a conjecture that is something like
> Fermat's Last Theorem, and is offering a prize for its proof or disproof.
>
> I believe the conjecture, called the Beal Conjecture, after the banker and
> amateur mathematician that discovered it, is as follows.
>
> Given A,B,C,x,y,z whole numbers, x,y,z > 2. If A^x + B^y = C^z, then A, B, C
> have a common factor.
>
> The only examples I could generate in a few minutes of playing with a
> spreadsheet are 32^3 + 8^5 = 16^4, and 15^4 + 15^5 = 30^4.
>
> If you let the exponents include 2, then 13^2 + 3^3 = 14^2 is a
> counterexample. Proving the Beal Conjecture would be another way to prove
> Fermat's Last Theorem.
>
> Anyway you may want to check out the article yourself.
>
> Phil Mahler
> Middlesex CC
> Bedford, MA
>
> p.s. As I was searching for examples, with a TV on nearby, Star Trek - Next
> Generation came on - an old episode obviously. At the beginning, the captain
> was playing with Fermat's Last Theorem on his computer.
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A. Jorge Garcia Teacher/Professor Mathematics/CompSci BaldwinSHS/NassauCC
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