Reducibility of translates of Dickson polynomials
نویسندگان
چکیده
منابع مشابه
Reducibility of Polynomials
Reducibility without qualification means in this lecture reducibility over the rational field. Questions on such reducibility occupy an intermediate place between questions on reducibility of polynomials over an algebraically closed field and those on primality. I shall refer to these two cases as to the algebraic and the arithmetic one and I shall try to exhibit some of the analogies consideri...
متن کاملOn Modified Dickson Polynomials
were defined and studied by P. Fllipponi In the case a-\ in [1], where several identities and congruences were established. In this note we generalize some of those theorems and present some new properties of these polynomials. One basic result is Proposition 2 in [1] which states that if/? is an odd prime and k is an integer, then Zp(k,l) = (k\p) (mod/0, (1-2) where (k \p) is the Legendre symb...
متن کاملDickson Polynomials That Are Permutations
A theorem of S.D. Cohen gives a characterization for Dickson polynomials of the second kind that permutes the elements of a finite field of cardinality the square of the characteristic. Here, a different proof is presented for this result. 1. Permutation polynomials of finite fields. In recent years cryptographers became interested in finding polynomials that induce a bijection of a finite fiel...
متن کاملDembowski-Ostrom polynomials from Dickson polynomials
Motivated by several recent results, we determine precisely when Fk(X , a)− Fk(0, a) is a Dembowski-Ostrom polynomial, where Fk(X, a) is a Dickson polynomial of the first or second kind. As a consequence, we obtain a classification of all such polynomials which are also planar; all examples found are equivalent to previously known examples.
متن کاملExponential sums with Dickson polynomials
We give new bounds of exponential sums with sequences of iterations of Dickson polynomials over prime finite fields. This result is motivated by possible applications to polynomial generators of pseudorandom numbers. © 2004 Elsevier Inc. All rights reserved.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1998
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-98-04363-9