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Given a function f : A → A, let f k denote the composition of f with itself k times. It is easy to verify that there are exactly 10 permutations f: {1,2,3,4} → {1,2,3,4} such that f 10(x) = x for all x. This month's problem is to find all k such that there are exactly k permutations f : {1,2,...,n} → {1,2,...,n} such that f k(x) = x for all x. Please do this for n from 1 to 8 inclusive.
The solution will be posted shortly.
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