Factorization properties of chebyshev polynomials

On Some Classes of Permutation Polynomials

“…Under given conditions for p, by Theorem 7 of [7] we know that E l−1 (x) splits in F p [x]. So η t + η −t ∈ F p and thus by Lemma 5.1 we have (E k (η t + η −t )) s = 1.…”

On Difference Quotients of Chebyshev Polynomials

“…However due to numerical evidences, one may conjecture that for a ∈ Z and a = ±1, QT p (a, z) is an irreducible polynomial over Z. If this is true, it will be a generalization of a well known fact that for an odd integer n, n is a prime if and only Tn(z) z is an irreducible polynomial over Z (See Theorem 3 of [7]) because T p (0) = 0. This remains an open problem.…”

The Galois theory of the lemniscate

“…For further results on the factorization of Chebyshev polynomials, see [8]. There is also another interesting analogy to consider, this one involving the Carlitz polynomials [M ](X) for M ∈ F p [T ][X].…”