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Topic: Fermat's last for generalised integers (Read 1428 times) |
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JocK
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Fermat's last for generalised integers
« on: Jun 24th, 2005, 12:15pm » |
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Does the equation x^3 + y^3 = z^3 have a solution in non-zero Eisenstein integers?
The similar question for Gaussian integers still seems to be unanswered: as far as I know it has not been proven that non-zero Gaussian integer solutions fail to exist, but also no example of such a solution is yet known.
So, I was wondering: "How much further do we need to go along the road of generalised integers before solutions do appear?"
The first reasonable step beyond Gaussian integers could be the Eisenstein integers that fill the complex plane denser than the Gaussian integers.
(The next step: Hamiltonian integers?  )
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| « Last Edit: Jun 24th, 2005, 1:30pm by JocK » |
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solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
xy - y = x5 - y4 - y3 = 20; x>0, y>0.
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Barukh
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Re: Fermat's last for generalised integers
« Reply #1 on: Jun 25th, 2005, 9:28am » |
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Sources tell that your first quesition was answered in negative by Gauss. I haven't seen the proof though.
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