If $x+y+z \equiv 1 \pmod{17}$, where $x,y,z$ are irrationals, then is it true that $x^n + y^n +z^n \equiv 1 \pmod{17}$ for odd $n$?
Prove that $\alpha^n+\beta^n+\gamma^n \equiv 4^n+5^n+(-6)^n \pmod{17}$