{"status": "success", "data": {"description_md": "**POTD 2024-01-24**\n\nLet $p(x)$ be a polynomial with real coefficients and of degree at most $2023$ such that $p(x)=\\frac{\\lfloor x^2 \\rfloor}{2}$ for $x=1,2,3 \\ldots 2024$. If $N$ is the remainder when $p(0)+p(2025)$ is divided by $1000$, find $N$.", "description_html": "<p><strong>POTD 2024-01-24</strong></p>&#10;<p>Let <span class=\"katex--inline\">p(x)</span> be a polynomial with real coefficients and of degree at most <span class=\"katex--inline\">2023</span> such that <span class=\"katex--inline\">p(x)=\\frac{\\lfloor x^2 \\rfloor}{2}</span> for <span class=\"katex--inline\">x=1,2,3 \\ldots 2024</span>. If <span class=\"katex--inline\">N</span> is the remainder when <span class=\"katex--inline\">p(0)+p(2025)</span> is divided by <span class=\"katex--inline\">1000</span>, find <span class=\"katex--inline\">N</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "Problem of the Day #50", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}