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suyver
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"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?
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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