{"status": "success", "data": {"description_md": "It is given that $\\log_{6}a+\\log_{6}b+\\log_{6}c=6,$ where $a,$ $b,$ and $c$ are positive integers that form an increasing geometric sequence and $b-a$ is the square of an integer. Find $a+b+c.$\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>It is given that <span class=\"katex--inline\">\\log_{6}a+\\log_{6}b+\\log_{6}c=6,</span> where <span class=\"katex--inline\">a,</span> <span class=\"katex--inline\">b,</span> and <span class=\"katex--inline\">c</span> are positive integers that form an increasing geometric sequence and <span class=\"katex--inline\">b-a</span> is the square of an integer. Find <span class=\"katex--inline\">a+b+c.</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": 3, "problem_name": "2002 AIME II Problem 3", "can_next": true, "can_prev": true, "nxt": "/problem/02_aime_II_p04", "prev": "/problem/02_aime_II_p02"}}