Let $x,y,z$ be complex numbers such that
$$x+y+z = x^{5}+y^{5}+z^{5} = 0, \hspace{10pt} x^3+y^3+z^3=2$$
Find all possible values of
$$x^{2007}+y^{2007}+z^{2007}$$
Let $x,y,z$ be complex numbers such that
$$x+y+z = x^{5}+y^{5}+z^{5} = 0, \hspace{10pt} x^3+y^3+z^3=2$$
Find all possible values of
$$x^{2007}+y^{2007}+z^{2007}$$