{"status": "success", "data": {"description_md": "**POTD June 15, 2024**\n\nIf\n    $$\\prod\\limits_{n=0^\\circ}^{44^\\circ}\\sqrt{4\\left(\\dfrac{1+\\cos\\left(2n+1^\\circ\\right)}{2}\\right)\\left(1+\\cos\\left(\\dfrac{2n+1^\\circ}{2}\\right)\\right)\\left(1-\\cos\\left(\\dfrac{2n+1^\\circ}{2}\\right)\\right)} $$\n    \ncan be expressed as $\\frac{a}{(\\sqrt{b})^c}$, where $a, b, c \\in \\mathbb{Z}^+$, and $b$ is not divisible by the square of any prime, find $a+b+c$.", "description_html": "<p><strong>POTD June 15, 2024</strong></p>&#10;<p>If<br/>&#10;<span class=\"katex--display\">\\prod\\limits_{n=0^\\circ}^{44^\\circ}\\sqrt{4\\left(\\dfrac{1+\\cos\\left(2n+1^\\circ\\right)}{2}\\right)\\left(1+\\cos\\left(\\dfrac{2n+1^\\circ}{2}\\right)\\right)\\left(1-\\cos\\left(\\dfrac{2n+1^\\circ}{2}\\right)\\right)}</span></p>&#10;<p>can be expressed as <span class=\"katex--inline\">\\frac{a}{(\\sqrt{b})^c}</span>, where <span class=\"katex--inline\">a, b, c \\in \\mathbb{Z}^+</span>, and <span class=\"katex--inline\">b</span> is not divisible by the square of any prime, find <span class=\"katex--inline\">a+b+c</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "Problem of the Day #188", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}