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Let σ\sigmaσ be a permutation of {1,2,3,…,100}\{1, 2, 3, \ldots, 100\}{1,2,3,…,100}. Then there exists a smallest positive integer f(σ)f(\sigma)f(σ) such that σf(σ)=id\sigma^{f(\sigma)} = \text{id}σf(σ)=id, where id\text{id}id is the identity permutation.
What is the largest value of f(σ)f(\sigma)f(σ) over all σ?\sigma?σ?
Note: σk\sigma^kσk is σ\sigmaσ applied kkk times in succession.
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