Extended Fermat's Last Theorem - Slightly Off-topic
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.
Hey Ricardo- The AMS maintains an online catalog of classic "Theorems" (i.e., the unproven ones), Hypotheses and Conjectures (Hilbert's, Courant's, Fermat's, etc.), their current tatus, and a rough outline of the accepted or proposed proof, demonstration, or numerical simulation. They also include lots of re-statements of classic problems that make them appear to be different. I think the URL is www.ams.org, but that's just my opinion, and I could be wrong. D. Freed ----- Original Message ----- From: "Ricardo M. Forno" <rforno@tutopia.com> To: <fractint@mailman.xmission.com> Sent: Friday, August 16, 2002 11:44 PM Subject: [Fractint] Extended Fermat's Last Theorem - Slightly Off-topic
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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"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.
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 :-)"
participants (4)
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bmc1 -
dirving＠box.net.au -
Morgan L. Owens -
Ricardo M. Forno