{"status": "success", "data": {"description_md": "Find the largest prime number $p<1000$ for which there exists a complex number $z$ satisfying<br><br>the real and imaginary part of $z$ are both integers;<br>$|z|=\\sqrt{p}$, and<br>there exists a triangle whose three side lengths are $p$, the real part of $z^{3}$, and the imaginary part of $z^{3}$.<br><br>\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>Find the largest prime number <span class=\"katex--inline\">p&lt;1000</span> for which there exists a complex number <span class=\"katex--inline\">z</span> satisfying<br/><br/>the real and imaginary part of <span class=\"katex--inline\">z</span> are both integers;<br/><span class=\"katex--inline\">|z|=\\sqrt{p}</span>, and<br/>there exists a triangle whose three side lengths are <span class=\"katex--inline\">p</span>, the real part of <span class=\"katex--inline\">z^{3}</span>, and the imaginary part of <span class=\"katex--inline\">z^{3}</span>.<br/><br/></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": 6, "problem_name": "2023 AIME I Problem 15", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/23_aime_I_p14"}}