{"status": "success", "data": {"description_md": "Define a sequence of functions recursively by $f_1(x) = |x-1|$ and $f_n(x)=f_{n-1}(|x-n|)$ for integers $n > 1$. Find the least value of $n$ such that the sum of the zeros of $f_n$ exceeds $500{,}000$.\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>Define a sequence of functions recursively by <span class=\"katex--inline\">f_1(x) = |x-1|</span> and <span class=\"katex--inline\">f_n(x)=f_{n-1}(|x-n|)</span> for integers <span class=\"katex--inline\">n &gt; 1</span>. Find the least value of <span class=\"katex--inline\">n</span> such that the sum of the zeros of <span class=\"katex--inline\">f_n</span> exceeds <span class=\"katex--inline\">500{,}000</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": 4, "problem_name": "2020 AIME II Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/20_aime_II_p09", "prev": "/problem/20_aime_II_p07"}}