{"status": "success", "data": {"description_md": "Positive integers $a$ and $b$ satisfy the condition $$\\log_2(\\log_{2^a}(\\log_{2^b}(2^{1000})))=0. $$ Find the sum of all possible values of $a+b$.\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>Positive integers <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span> satisfy the condition <span class=\"katex--display\">\\log_2(\\log_{2^a}(\\log_{2^b}(2^{1000})))=0.</span> Find the sum of all possible values of <span class=\"katex--inline\">a+b</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": "2013 AIME II Problem 2", "can_next": true, "can_prev": true, "nxt": "/problem/13_aime_II_p03", "prev": "/problem/13_aime_II_p01"}}