{"status": "success", "data": {"description_md": "A right rectangular prism $P$ (i.e., a rectangular parallelpiped) has sides of integral length $a, b, c,$ with $a\\le b\\le c.$ A plane parallel to one of the faces of $P$ cuts $P$ into two prisms, one of which is similar to $P,$ and both of which have nonzero volume. Given that $b=1995,$ for how many ordered triples $(a, b, c)$ does such a plane exist?\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>A right rectangular prism <span class=\"katex--inline\">P</span> (i.e., a rectangular parallelpiped) has sides of integral length <span class=\"katex--inline\">a, b, c,</span> with <span class=\"katex--inline\">a\\le b\\le c.</span> A plane parallel to one of the faces of <span class=\"katex--inline\">P</span> cuts <span class=\"katex--inline\">P</span> into two prisms, one of which is similar to <span class=\"katex--inline\">P,</span> and both of which have nonzero volume. Given that <span class=\"katex--inline\">b=1995,</span> for how many ordered triples <span class=\"katex--inline\">(a, b, c)</span> does such a plane exist?</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": 5, "problem_name": "1995 AIME Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/95_aime_p12", "prev": "/problem/95_aime_p10"}}