2018 OIM Problems/Problem 1

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Problem

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

\[x_1 = (x_2 + x_3 + x_4 + \cdots + x_n)^{2018}\] \[x_2 = (x_1 + x_3 + x_4 + \cdots + x_n)^{2018}\] \[\cdots\] \[x_n = (x_1 + x_2 + x_3 + \cdots + x_{n-1})^{2018}\]

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

OIM Problems and Solutions