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B5

Part of 2023 Putnam

Problems(1)

2023 Putnam B5

Source:

12/3/2023
Determine which positive integers nn have the following property: For all integers mm that are relatively prime to nn, there exists a permutation π:{1,2,…,n}→{1,2,…,n}\pi:\{1,2, \ldots, n\} \rightarrow\{1,2, \ldots, n\} such that π(π(k))≡mk( mod n)\pi(\pi(k)) \equiv m k(\bmod n) for all k∈{1,2,…,n}k \in\{1,2, \ldots, n\}.
PutnamPutnam 2023