Solve $x^5 + y^5 + z^5 = 2015$ If $x, y, z$ are integer numbers, solve:
$$x^5 + y^5 + z^5 = 2015$$
A friend of mine claims there is no known solution, and, at the same time, there is no proof that there is no solution, but I do not believe him. However, I wasn't able to make much progress disproving his claim.
I tried modular arithmetics, but couldn't reach useful conclusion.

A very quick exhaustive computer search (for $0 \le x, y, z \leq \lceil 2015^.2 \rceil = 5$) shows there is no solution, as does a search with $0 \le x \le 200$ and $-200 \le y, z, \le 200$.
