OIM 2018 Problem 1

For each integer $n \ge 2$ , find all integer solutions of the following system of equations:

$$x_1 = (x_2 + x_3 + x_4 + ... + x_n)^{2018}$$ $$x_2 = (x_1 + x_3 + x_4 + ... + x_n)^{2018}$$ $$\vdots$$ $$x_n = (x_1 + x_2 + x_3 + ... + x_{n - 1})^{2018}$$