{"status": "success", "data": {"description_md": "Except for the first two terms, each term of the sequence $1000, x, 1000-x,\\ldots$ is obtained by subtracting the preceding term from the one before that. The last term of the sequence is the first negative term encounted. What positive integer $x$ produces a sequence of maximum length?\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>Except for the first two terms, each term of the sequence <span class=\"katex--inline\">1000, x, 1000-x,\\ldots</span> is obtained by subtracting the preceding term from the one before that. The last term of the sequence is the first negative term encounted. What positive integer <span class=\"katex--inline\">x</span> produces a sequence of maximum length?</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": "1998 AIME Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/98_aime_p09", "prev": "/problem/98_aime_p07"}}