{"status": "success", "data": {"description_md": "There exist $r$ unique nonnegative integers $n_1 > n_2 > \\cdots > n_r$ and $r$ unique integers $a_k$ $( 1\\le k\\le r)$ with each $a_k$ either $1$ or $- 1$ such that<br>\n$$ a_13^{n_1} + a_23^{n_2} + \\cdots + a_r3^{n_r} = 2008.$$Find $n_1 + n_2 + \\cdots + n_r$.\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>There exist <span class=\"katex--inline\">r</span> unique nonnegative integers <span class=\"katex--inline\">n_1 &gt; n_2 &gt; \\cdots &gt; n_r</span> and <span class=\"katex--inline\">r</span> unique integers <span class=\"katex--inline\">a_k</span> <span class=\"katex--inline\">( 1\\le k\\le r)</span> with each <span class=\"katex--inline\">a_k</span> either <span class=\"katex--inline\">1</span> or <span class=\"katex--inline\">- 1</span> such that<br/><br/>&#10;<span class=\"katex--display\"> a_13^{n_1} + a_23^{n_2} + \\cdots + a_r3^{n_r} = 2008.</span>Find <span class=\"katex--inline\">n_1 + n_2 + \\cdots + n_r</span>.</p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2008 AIME II Problem 4", "can_next": true, "can_prev": true, "nxt": "/problem/08_aime_II_p05", "prev": "/problem/08_aime_II_p03"}}