# System of Sums Of Powers

Algebra Level 4

Given the following system of equations:

\begin{align} x + y + z &= 1\\ x^{2} + y^{2} + z^{2} &= 2\\ x^{3} + y^{3} + z^{3} &= 3, \end{align}

find the smallest positive integer value of $$n ~(> 3)$$ such that $$x^{n} + y^{n} + z^{n}$$ is an integer.

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