{"status": "success", "data": {"description_md": "**POTD February 21, 2024**\n\nFor polynomial $P(x)=1-\\dfrac{5}{3}x+x^{2}$, define $Q(x)=P(x) \\cdot P(x^{3}) \\cdot P(x^{5}) \\cdot P(x^{7}) \\cdot P(x^{9})=\\sum\\limits_{i=0}^{50} a_i \\cdot x^{i}$. Then $\\sum\\limits_{i=0}^{50} |a_i|=\\dfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.", "description_html": "<p><strong>POTD February 21, 2024</strong></p>&#10;<p>For polynomial <span class=\"katex--inline\">P(x)=1-\\dfrac{5}{3}x+x^{2}</span>, define <span class=\"katex--inline\">Q(x)=P(x) \\cdot P(x^{3}) \\cdot P(x^{5}) \\cdot P(x^{7}) \\cdot P(x^{9})=\\sum\\limits_{i=0}^{50} a_i \\cdot x^{i}</span>. Then <span class=\"katex--inline\">\\sum\\limits_{i=0}^{50} |a_i|=\\dfrac{m}{n}</span>, where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are relatively prime positive integers. Find <span class=\"katex--inline\">m+n</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #75", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}