Re: FLT an incurable, unending addiction


fermat wrote:
> Hello to all those here with a bright mind and a friendly nature. Your
> fine works make the world a better place and are deeply appreciated by
> many folks here and around the world.
>
> The great FLT problem having been solved, but with a general proof
> intellectually inaccessible to many, it would seem that a simpler
> solution would be desireable. For example, I am wondering if it would
> be helpful, or significant, were a proof of the first case using only
> basic college algebra be presented here? (If such has not already been
> done, that is)

Hi, "fermat"/DS:

As you may know, the terminology "first case" in connection with
Fermat's Last Theorem has historically a specific meaning, i.e. the
exponent is relatively prime to each term. or if we reduce to cases
of odd prime exponent p, that none of x,y,z is divisible by p, yet:

x^p + y^p = z^p

Sophie Germain proved (*) the "first case" of FLT when p and 2p+1
are both primes, a line of attack which was extended by Legendre
and others. Primes p such that 2p+1 is also prime were afterward
known as Sophie Germain primes.

Perhaps you have in mind something of this sort? Given that any
common factor of x,y,z may be removed from a solution, "second
case" in connection with FLT has the conventional meaning that
p divides _exactly one_ of x,y,z.

regards, chip

(*) Meaning that she proved no solutions of this kind exist.

.