2018 OIM Problems/Problem 1
Problem
For each natural number 
, find the integer solutions to the following system of equations:
![\[x_1 = (x_2 + x_3 + x_4 + \cdots + x_n)^{2018}\]](http://latex.artofproblemsolving.com/9/7/6/976ec96e27cdf62dd7f5f4188fdf3c8ba8061a99.png)
![\[x_2 = (x_1 + x_3 + x_4 + \cdots + x_n)^{2018}\]](http://latex.artofproblemsolving.com/c/2/0/c202b390c5a43445f5c2067207dd12b01455a177.png)
![\[\cdots\]](http://latex.artofproblemsolving.com/c/e/2/ce26e72ef1985f46ac9b2fedbe0879501540c94c.png)
![\[x_n = (x_1 + x_2 + x_3 + \cdots + x_{n-1})^{2018}\]](http://latex.artofproblemsolving.com/5/2/c/52ca3c90da4c678058ce4b84c45d6b2340ff3387.png)
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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