Yeah sure.. Newton's Sums..

Algebra Level 5

Let \((x_1, y_1, z_1)\), \((x_2, y_2, z_2)\), \(\dots\), \((x_n, y_n, z_n)\) be the rational solutions to the following system of equations

\[x+y+z=0 \\ x^3 + y^3 + z^3 =18 \\ x^7 + y^7 + z^7 =2058\]


\[\sum_{i=1}^{n} x_{i}y_{i}z_{i}\]

  • The triple \((a, b, c)\) and \((c, a, b)\) are considered to be different.
  • This problem is not entirely original.

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