A nonlinear system of algebraic equations

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

[tex]\sum^{m}_{i=1}x^{n}_{i}=k_{n}[/tex]

[tex]n=0,1,2...[/tex]

[tex]m<\infty[/tex]

[tex]\sum^{m}_{i=1}x^{n}_{i}[/tex]

is a power sum polynomial
 

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is it even possible to solve this system ?
 

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