A set $C$ is *convex* if for all $x,y \in C$ and for all $\alpha \in [0,1]$ the point $\alpha x + (1-\alpha) y \in C$.
There are no natural numbers $\naturals = (1, 2, 3, \ldots)$ $x$, $y$, and $z$ such that $x^n + y^n = z^n$, in which $n$ is a natural number greater than 2.