Re: Even Periods in Fermat's Last Theorem and Modular Arithmetic (FLTMA)

On 31 Jul 2005 18:41:22 -0700, DGoncz@xxxxxxx wrote:

>I wrote:
>0<n<a<b<c<(a+b)
>
>I meant:
>0<n,a,b,c;a<b<c<(a+b)
>
>Doug

Try testing one aspect of your idea for n=3.

See if you can find integers a,b,c satisfying your inequalities and
also the 3 congruences:

a^3+b^3=0 mod c
c^3-a^3=0 mod b
c^3-b^3=0 mod a

If you find them, wouldn't that put you back to square 1?

By the way, did you ever use the inequalities a<b<c<a+b? If it plays
no role in your proof, why even state it?

Finally, if you find solutions to the above congruences, check if in
all cases. s.n=0 mod abc. If even one case fails, then you can't
assert s.n = 0 mod abc.

The case n=3 is a good test case for proposed elementary attacks on
FLT. If it doesn't work for n=3 then the attack is flawed, and if it
does work, then that's already a worthwhile discovery since, as far as
I know, there are no known elementary proofs of FLT for n=3 (all use
algebraic number theory).

quasi
.

Relevant Pages
Quantcast