SpecialEquation Function Intermediate

Problem - 2422
Solve the following system in integers: $$ \left\{ \begin{array}{ll} x_1 + x_2 + \cdots + x_n &= n \\ x_1^2 + x_2^2 + \cdots + x_n^2 &= n \\ \cdots\\ x_1^n + x_2^n + \cdots + x_n^n &= n \end{array} \right. $$

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