{"status": "success", "data": {"description_md": "Let $\\mathcal{S}$ be the set of all functions $f: \\mathbb{Z} \\longrightarrow \\mathbb{R}$ such that $f(x+2024) - 2024 \\le f(x) \\le f(x+2277) - 2277$ for all $x \\in \\mathbb{Z}$, and $f(1) = 1$. Find the minimum integer $k > 1$ such that $f(k)$ is the same across all $f \\in \\mathcal{S}$.", "description_html": "<p>Let <span class=\"katex--inline\">\\mathcal{S}</span> be the set of all functions <span class=\"katex--inline\">f: \\mathbb{Z} \\longrightarrow \\mathbb{R}</span> such that <span class=\"katex--inline\">f(x+2024) - 2024 \\le f(x) \\le f(x+2277) - 2277</span> for all <span class=\"katex--inline\">x \\in \\mathbb{Z}</span>, and <span class=\"katex--inline\">f(1) = 1</span>. Find the minimum integer <span class=\"katex--inline\">k &gt; 1</span> such that <span class=\"katex--inline\">f(k)</span> is the same across all <span class=\"katex--inline\">f \\in \\mathcal{S}</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "Christmas Contest - Individual Round - Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/christmas1_individual-p19", "prev": "/problem/christmas1_individual-p17"}}