{"status": "success", "data": {"description_md": "A function $f$ is defined for all real numbers and satisfies $$f(2 + x) = f(2 - x)\\qquad\\text{and}\\qquad f(7 + x) = f(7 - x) $$for all real $x$. If $x = 0$ is a root of $f(x) = 0$, what is the least number of roots $f(x) = 0$ must have in the interval $-1000 \\le x \\le 1000$?\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>A function <span class=\"katex--inline\">f</span> is defined for all real numbers and satisfies <span class=\"katex--display\">f(2 + x) = f(2 - x)\\qquad\\text{and}\\qquad f(7 + x) = f(7 - x)</span>for all real <span class=\"katex--inline\">x</span>. If <span class=\"katex--inline\">x = 0</span> is a root of <span class=\"katex--inline\">f(x) = 0</span>, what is the least number of roots <span class=\"katex--inline\">f(x) = 0</span> must have in the interval <span class=\"katex--inline\">-1000 \\le x \\le 1000</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": "1984 AIME Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/84_aime_p13", "prev": "/problem/84_aime_p11"}}