Polynomial cycles in certain local domains

1. Let R be a domain and f ∈ R[X] a polynomial. A k-tuple $x₀,x₁,...,x_{k-1}$ of distinct elements of R is called a cycle of f if $f(x_i) = x_{i+1}$ for i=0,1,...,k-2 and $f(x_{k-1}) = x₀$. The number k is called the length of the cycle. A tuple is a cycl

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