{"status": "success", "data": {"description_md": "**POTD November 2, 2024**\n\nLet $p$ be the unique polynomial of degree 6 such that\n$$p(n) = (-1)^n \\binom{6}{n}$$ for $n = 0$, $1$, $2$, $3$, $\\ldots$ , $6$. What is $p(7)$?", "description_html": "<p><strong>POTD November 2, 2024</strong></p>&#10;<p>Let <span class=\"katex--inline\">p</span> be the unique polynomial of degree 6 such that<br/>&#10;<span class=\"katex--display\">p(n) = (-1)^n \\binom{6}{n}</span> for <span class=\"katex--inline\">n = 0</span>, <span class=\"katex--inline\">1</span>, <span class=\"katex--inline\">2</span>, <span class=\"katex--inline\">3</span>, <span class=\"katex--inline\">\\ldots</span> , <span class=\"katex--inline\">6</span>. What is <span class=\"katex--inline\">p(7)</span>?</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "Problem of the Day #319", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}