On solving equations of algebraic sum of equal powers (Q867770)

The authors are interested in the system of equations \[ x_1^j+x_2^j+\ldots+x_k^j-x_{k+1}^j-x_{k+2}^j-\ldots-x_n^j=p_j, \] for \(j=1,\ldots,n\). They reduce it to two equations, the first of degree \(k\), and the second of degree \(n-k\).