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Integer system of equations

Source: Iberoamerican 2018 Problem 1

September 26, 2018
algebrasystem of equations

Problem Statement

For each integer n≥2n \ge 2, find all integer solutions of the following system of equations:
x1=(x2+x3+x4+...+xn)2018x_1 = (x_2 + x_3 + x_4 + ... + x_n)^{2018} x2=(x1+x3+x4+...+xn)2018x_2 = (x_1 + x_3 + x_4 + ... + x_n)^{2018} ⋮\vdots xn=(x1+x2+x3+...+xn−1)2018x_n = (x_1 + x_2 + x_3 + ... + x_{n - 1})^{2018}
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