TITLE: Fermat Last Theorem for non Integer Exponents
QUESTION [28 upvotes]: We now that Fermat's last theorem is true so there are not positive integer solutions to
$$x^n+y^n=z^n$$
for $n\in\mathbb{N}$ and $n>2$.
But what about if $n\in\mathbb{R}$ or $n\in\mathbb{R}^+$?

REPLY [9 votes]: $1782^n + 1841^n = 1922^n$ with $n \approx 11.999999995097161$