{"status": "success", "data": {"description_md": "For each integer $n\\ge 3$, let $f(n)$ be the number of 3-element subsets of the vertices of a regular $n$-gon that are the vertices of an isosceles triangle (including equilateral triangles). Find the sum of all values of $n$ such that $f(n+1)=f(n)+78$.\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>For each integer <span class=\"katex--inline\">n\\ge 3</span>, let <span class=\"katex--inline\">f(n)</span> be the number of 3-element subsets of the vertices of a regular <span class=\"katex--inline\">n</span>-gon that are the vertices of an isosceles triangle (including equilateral triangles). Find the sum of all values of <span class=\"katex--inline\">n</span> such that <span class=\"katex--inline\">f(n+1)=f(n)+78</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": 6, "problem_name": "2017 AIME II Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/17_aime_II_p14", "prev": "/problem/17_aime_II_p12"}}