greetings . is there a general method-algorithm to solve the following system !?


$\sum\_{n=1}^{m} {x\_{n}}^{j}= {k}\_{j} $


$j=1,2,...,m$


$k\_{j}$ are constants 


thanks in advance 



a system of nonlinear equations (power sum) 
Solution of this system are ALL m roots of the polynomial equation P(x) = 0 in ONE variable.
Where P(x) is defined as follows.


Power sum related to elementary symmetric functions by the so-called Newton formulas.
$\sigma\_i = Newton (p\_i)$


<http://en.wikipedia.org/wiki/Newton>'s\_identities


So define $c\_i= Newton(k\_j)$.


And write polynom $P(x) = \sum\_i c\_i x^i$


Its zeros are yours numbers $x\_i$.


To solve polynomial equation you may use Newton method or any other method.


