{"status": "success", "data": {"description_md": "Let $\\omega=\\cos\\frac{2\\pi}{7}+i\\cdot\\sin\\frac{2\\pi}{7}$, where $i=\\sqrt{-1}$. Find<br>\n$$\\prod_{k=0}^{6}(\\omega^{3k}+\\omega^k+1). $$\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>Let <span class=\"katex--inline\">\\omega=\\cos\\frac{2\\pi}{7}+i\\cdot\\sin\\frac{2\\pi}{7}</span>, where <span class=\"katex--inline\">i=\\sqrt{-1}</span>. Find<br/><span class=\"katex--display\">\\prod_{k=0}^{6}(\\omega^{3k}+\\omega^k+1).</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": "2023 AIME II Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/23_aime_II_p09", "prev": "/problem/23_aime_II_p07"}}