{"status": "success", "data": {"description_md": "There are nonzero integers $a$, $b$, $r$, and $s$ such that the complex number $r+si$ is a zero of the polynomial $P(x) = x^3 - ax^2 + bx - 65$. For each possible combination of $a$ and $b$, let $p_{a,b}$ be the sum of the zeroes of $P(x)$. Find the sum of the $p_{a,b}$'s for all possible combinations of $a$ and $b$.\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>There are nonzero integers <span class=\"katex--inline\">a</span>, <span class=\"katex--inline\">b</span>, <span class=\"katex--inline\">r</span>, and <span class=\"katex--inline\">s</span> such that the complex number <span class=\"katex--inline\">r+si</span> is a zero of the polynomial <span class=\"katex--inline\">P(x) = x^3 - ax^2 + bx - 65</span>. For each possible combination of <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span>, let <span class=\"katex--inline\">p_{a,b}</span> be the sum of the zeroes of <span class=\"katex--inline\">P(x)</span>. Find the sum of the <span class=\"katex--inline\">p_{a,b}</span>'s for all possible combinations of <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</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 I Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/13_aime_I_p11", "prev": "/problem/13_aime_I_p09"}}