{"status": "success", "data": {"description_md": "The harmonic mean of two positive numbers is the reciprocal of the arithmetic mean of their reciprocals. For how many ordered pairs of positive integers $(x,y)$ with $x<y$ is the harmonic mean of $x$ and $y$ equal to $6^{20}.$\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 harmonic mean of two positive numbers is the reciprocal of the arithmetic mean of their reciprocals. For how many ordered pairs of positive integers <span class=\"katex--inline\">(x,y)</span> with <span class=\"katex--inline\">x&lt;y</span> is the harmonic mean of <span class=\"katex--inline\">x</span> and <span class=\"katex--inline\">y</span> equal to <span class=\"katex--inline\">6^{20}.</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": 4, "problem_name": "1996 AIME Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/96_aime_p09", "prev": "/problem/96_aime_p07"}}