Chebyshev Mappings of Finite Fields
Chebyshev Mappings of Finite Fields
For a fixed prime p, we consider the set of maps ℤ⁄pℤ → ℤ⁄pℤ of the form a ↦ Tn(a), where Tn(x) is the degree-n Chebyshev polynomial of the first kind. We observe that these maps form a semigroup, and we determine its size and structure.