{"status": "success", "data": {"description_md": "For distinct complex numbers $z_1,z_2,\\ldots,z_{673}$, the polynomial \n$$ (x-z_1)^3(x-z_2)^3 \\cdots (x-z_{673})^3 $$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 \n$$ \\left| \\sum_{1 \\le j For distinct complex numbers z_1,z_2,\\ldots,z_{673}, the polynomial (x-z_1)^3(x-z_2)^3 \\cdots (x-z_{673})^3 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 <k \\le 673} z_jz_k \\right| can be expressed in the form \\tfrac{m}{n}, where m and n are relatively prime positive integers. Find m+n.
Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.