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Something with a lot of ! is integer

Source: 2022 IMOC N1

September 5, 2022
number theoryIMOC

Problem Statement

Find all positive integer nn such that for all i=1,2,⋯ ,ni=1,2,\cdots,n, n!i!(n−i+1)!\frac{n!}{i!(n-i+1)!} is an integer.
Proposed by ckliao914
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