(adsbygoogle = window.adsbygoogle || []).push({}); "Extended" Fermat's last theorem.

Just to satisfy my own curiousity:

FLT states that there are no [itex]n\in{\mathbb N}[/itex] such that

[tex]x^n+y^n=z^n[/tex]

whenever [itex]n\geq 3[/itex] and [itex]x,y,z\in{\mathbb N}[/itex].

However, what would happen when I allow [itex]n[/itex] to be non-integer as well? Are there solutions if [itex]n\in{\mathbb Q}^+[/itex] or [itex]n\in{\mathbb R}^+[/itex] ? Will one be able to find a set [itex]x,y,z\in{\mathbb N}[/itex] and an [itex]n\geq 3[/itex] such that this "extended" FLT holds?

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# Extended Fermat's last theorem.

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