PUMaC 2022 · 个人决赛（A 组） · 第 1 题

1. Let f : Z → Z be a function which satisfies k | f ( x ) − x for all k, x ∈ Z and f ( x ) − x ≤

0 > 0 > 0

2023. If f (1) = 2000, what can f be? k Remark: Here, f ( x ) denotes the k -fold application of f to x .