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Sep 24, 2014 at 6:09 comment added Joël RW means that $x^n$ is the hyper-volume of an hypercube of size $x$ in an Euclidean space of dimension $n$. Fermat Last Theorem is the statement that in dimension $n \geq 3$, the sum of the volumes of two hypercubes with side of (positive) integral length is not the volume of such an hypercupe. The same statement fails in dimensions $n = 2$ and $n=1$.
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Sep 23, 2014 at 2:54 comment added S. Carnahan What does this have to do with vector spaces of increasing dimension? The Fermat curve of degree $n$ defined by $x^n + y^n = z^n$ is an algebraic plane curve.
S Sep 23, 2014 at 2:41 history answered R W CC BY-SA 3.0
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