Show that the Diophantine equation only have trivial solution

Question

Let the Diophantine equation be $x^2 + y^2 = cz^2$ for $c = 6 \mod 8$, show that this equations only have trivial solution $(0,0,0)$. I can show this for the case that $c = 6$ but for the general one, I tried using the fact that $cz^2 \in \{ 0,6 \} \mod 8$ but this leads nowhere. Any advice ?