Re: [MATHEDCC] Just when you thought it was safe to go back in the water...

Alvar J. Garcia (aj317@FREENET.BUFFALO.EDU)
Wed, 26 Nov 1997 19:22:27 -0500 (EST)

My difficulty with this is the way the conjecture is stated. As in the
statement of Fermat's Last theorem many say thus: x^n+y^n=z^n has no
solutions for n an integer greater than 2 and x,y,z are whole numbers.
The problem is that this allows for degenerate cases such as 0^3+0^3=0^3
or (-2)^6+0^6=2^6. Isn't the correct statement of FLT that n>2 (all three
exponents are integers and equal to eachother) and x,y,z are unequal
positive integers?

Also, it has been stated that to prove the Beal Conjecture is to prove
FLT. Why so?

TIA,

On Tue, 25 Nov 1997, Alvar J. Garcia wrote:

> BTW, are A,B,C all unequal whole numbers?
>
> 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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A. Jorge Garcia Teacher/Professor Mathematics/CompSci BaldwinSHS/NassauCC
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