Question 139
Find all triples $(x, y, z)$ of integers such that
$$
x^{2} y + y^{2} z + z^{2} x = 2010^{2} \text{ and } x y^{2} + y z^{2} + z x^{2} = -2010.
$$
$$
x^{2} y + y^{2} z + z^{2} x = 2010^{2} \text{ and } x y^{2} + y z^{2} + z x^{2} = -2010.
$$