A nonlinear system of algebraic equations

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how to solve a nonlinear system of algebraic equations such as :

\sum^{m}_{i=1}x^{n}_{i}=k_{n}

n=0,1,2...

m<\infty

\sum^{m}_{i=1}x^{n}_{i}

is a power sum polynomial
 
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is it even possible to solve this system ?
 

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