Question 10
For distinct complex numbers $z_1,$ $z_2,$ $\ldots,$ $z_{673},$ the polynomial $$
\begin{gathered} (x - z_1)^3 (x - z_2)^3 \\ \cdots (x - z_{673})^3 \end{gathered}
$$ can be expressed as $x^{2019} + 20x^{2018}$ $+ 19x^{2017} + g(x),$ where $g(x)$ is a polynomial with complex coefficients and with degree at most $2016.$ The value of $$
\left| \sum_{1 \le j \lt k \le 673} z_j z_k \right|
$$ can be expressed in the form $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$
\begin{gathered} (x - z_1)^3 (x - z_2)^3 \\ \cdots (x - z_{673})^3 \end{gathered}
$$ can be expressed as $x^{2019} + 20x^{2018}$ $+ 19x^{2017} + g(x),$ where $g(x)$ is a polynomial with complex coefficients and with degree at most $2016.$ The value of $$
\left| \sum_{1 \le j \lt k \le 673} z_j z_k \right|
$$ can be expressed in the form $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$