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I am investigating solutions to Fermat's equation $$x^n + y^n = z^n$$ with $x,y,z$ in the Gaussian integers, excluding integers and pure imaginaries.

I have found out that there are only trivial solutions for the $n=3$ and $n=4$ cases, e.g. here.

I would be grateful if you let me know of the current status or if it is already a theorem.

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Please don't make posts where "the title says it all". The title is like the writing on the spine of a book; the contents of the post should be sufficient by themsleves. – Arturo Magidin Mar 11 '12 at 22:10
Maybe this should be moved to mathoverflow? – Ben Crowell Mar 11 '12 at 22:18
@Ben, now I am feeling the same. But Motizens feel that questions posted here should at least have a 24 hour life or more before they pass to the other elite society. – Herband Mar 11 '12 at 22:56
I have reposted this question on MO:… – Herband Mar 12 '12 at 10:12
This question has been answered on the bigger sister site. – Herband Mar 14 '12 at 15:19

As mentioned above in the comments, the question has been answered on MathOverflow: it's still an open problem.

(This answer is community wiki so that it won't generate any reputation.)

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