IIRC, a pair of Japanise (?) students proposed that all elliptic curves are also modular forms. Someone else pointed out that, assuming Fermat was wrong, his equation x^n + y^n = z^n would be an elliptic equation, and the corresponding modular form is decidedly weird. Yet ANOTHER mathematition later proved that this modular form is in fact too weird to actually exist. In other words, assuming that EVERY elliptic curve REALLY IS a modular form, Fermat's Last Theorum MUST be true. Andrew Wiles proved that elliptic curves ARE modular, and as a side effect proved Fermat right. Andrew. PS. I've read the book. And I'm kinda bored today...
From: "Morgan L. Owens" <packrat@nznet.gen.nz> Reply-To: fractint@mailman.xmission.com To: fractint@mailman.xmission.com, fractint@mailman.xmission.com Subject: Re: [Fractint] Extended Fermat's Last Theorem - Slightly Off-topic Date: Mon, 19 Aug 2002 13:43:43 +1200
At 01:09 19/08/2002, dirving@box.net.au wrote:
"Ricardo M. Forno" wrote:
Does someone in the list know if the following conjecture, that
includes as
a particular case Fermat's Last Theorem, has ever been posed, and proved false or true? x[1]^p + x[2]^p + ... x[n]^p = z^p, for x[i] > 0 and 1 < n < p, has no integer solutions. TIA.
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I would conjecture ... no.
Reasonable: a proof of this extended conjecture would in turn provide an alternatve proof of FLT as a special case.
So if there has been a proof, it has been found more recently than (and probably develops the ideas of) Wiles' tour de force.
Morgan L. Owens "Yes, Andrew; a corollary :-)"
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