Re: [math-fun] To VIctor Re: Mapping problem

that ideal — call it I_n — of all P(x) vanishing on every element of Z_n.

Question: What is I_n ??? P(x) is a P.I.D. so I_n must be generated by one polynomial, so a unique monic one. What is it ???

Then of course the distinct polynomials correspond to the quotient Z[x] / I_n. What does that look like?

*Then* we could start finding the cycle structure corresponding to each element of this quotient.

Well, no. If n is composite then we can not necessarily divide through by the leading coefficient. —Anonymous