{"status": "success", "data": {"description_md": "The numbers in the sequence 101, 104, 109, 116, $\\ldots$ are of the form $a_n = 100 + n^2$, where $n = 1$, 2, 3, $\\ldots$. For each $n$, let $d_n$ be the greatest common divisor of $a_n$ and $a_{n + 1}$. Find the maximum value of $d_n$ as $n$ ranges through the positive integers.\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>The numbers in the sequence 101, 104, 109, 116, <span class=\"katex--inline\">\\ldots</span> are of the form <span class=\"katex--inline\">a_n = 100 + n^2</span>, where <span class=\"katex--inline\">n = 1</span>, 2, 3, <span class=\"katex--inline\">\\ldots</span>. For each <span class=\"katex--inline\">n</span>, let <span class=\"katex--inline\">d_n</span> be the greatest common divisor of <span class=\"katex--inline\">a_n</span> and <span class=\"katex--inline\">a_{n + 1}</span>. Find the maximum value of <span class=\"katex--inline\">d_n</span> as <span class=\"katex--inline\">n</span> ranges through the positive integers.</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": "1985 AIME Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/85_aime_p14", "prev": "/problem/85_aime_p12"}}