Problem
Christmas Contest - Individual Round - Problem 18
Let S be the set of all functions f: \mathbb{Z} \longrightarrow \mathbb{R} s.t. 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 S.
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