{"status": "success", "data": {"description_md": "Let $S$ be the set of all polynomials of the form $z^3+az^2+bz+c$, where $a$, $b$, and $c$ are integers. Find the number of polynomials in $S$ such that each of its roots $z$ satisfies either $\\left\\lvert z \\right\\rvert = 20$ or $\\left\\lvert z \\right\\rvert = 13$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Let <span class=\"katex--inline\">S</span> be the set of all polynomials of the form <span class=\"katex--inline\">z^3+az^2+bz+c</span>, where <span class=\"katex--inline\">a</span>, <span class=\"katex--inline\">b</span>, and <span class=\"katex--inline\">c</span> are integers. Find the number of polynomials in <span class=\"katex--inline\">S</span> such that each of its roots <span class=\"katex--inline\">z</span> satisfies either <span class=\"katex--inline\">\\left\\lvert z \\right\\rvert = 20</span> or <span class=\"katex--inline\">\\left\\lvert z \\right\\rvert = 13</span>.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2013 AIME II Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/13_aime_II_p13", "prev": "/problem/13_aime_II_p11"}}