{"status": "success", "data": {"description_md": "Given a function $f$ for which<br>\n$$f(x)=f(398-x)=f(2158-x)=f(3214-x) $$holds for all real $x,$ what is the largest number of different values that can appear in the list $f(0),f(1),f(2),\\ldots,f(999)?$\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>Given a function <span class=\"katex--inline\">f</span> for which<br/><span class=\"katex--display\">f(x)=f(398-x)=f(2158-x)=f(3214-x) </span>holds for all real <span class=\"katex--inline\">x,</span> what is the largest number of different values that can appear in the list <span class=\"katex--inline\">f(0),f(1),f(2),\\ldots,f(999)?</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": "2000 AIME I Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/00_aime_I_p13", "prev": "/problem/00_aime_I_p11"}}