{"status": "success", "data": {"description_md": "Let\n$p(x,y) = a_0 + a_1x + a_2y + a_3x^2 + a_4xy + a_5y^2 + a_6x^3 + a_7x^2y + a_8xy^2 + a_9y^3$.\nSuppose that\n$p(0,0) = p(1,0) = p( - 1,0) = p(0,1) = p(0, - 1)$\n$p(1,1) = p(1, - 1) = p(2,2) = 0$\nThere is a point $\\left(\\tfrac {a}{c},\\tfrac {b}{c}\\right)$ for which $p\\left(\\tfrac {a}{c},\\tfrac {b}{c}\\right) = 0$ for all such polynomials, where $a$, $b$, and $c$ are positive integers, $a$ and $c$ are relatively prime, and $c > 1$. Find $a + b + c$.\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": "

Let
p(x,y) = a_0 + a_1x + a_2y + a_3x^2 + a_4xy + a_5y^2 + a_6x^3 + a_7x^2y + a_8xy^2 + a_9y^3.
Suppose that
p(0,0) = p(1,0) = p( - 1,0) = p(0,1) = p(0, - 1)
p(1,1) = p(1, - 1) = p(2,2) = 0
There is a point \\left(\\tfrac {a}{c},\\tfrac {b}{c}\\right) for which p\\left(\\tfrac {a}{c},\\tfrac {b}{c}\\right) = 0 for all such polynomials, where a, b, and c are positive integers, a and c are relatively prime, and c > 1. Find a + b + c.

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.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "2008 AIME I Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/08_aime_I_p14", "prev": "/problem/08_aime_I_p12"}}