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.

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The solution will be posted shortly.
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