On the number of solutions of equations of Dickson polynomials over finite fields

Wun Seng Chou, Gary L. Mullen, Bertram Wassermann

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Let k, n1, ..., nk be fixed positive integers, c1, ..., ck ∈ GF(q)*, and a1, ..., ak, c ∈ GF(q). We study the number of solutions in GF(q) of the equation c1Dn1(x1, a1)+c2Dn2(x2, a2)+...+ckDnk(xk, ak) = c, where each Dni(xi, ai), 1 ≤ i ≤ k, is the Dickson polynomial of degree ni with parameter ai. We also employ the results of the k = 1 case to recover the cardinality of preimages and images of Dickson polynomials obtained earlier by Chou, Gomez-Calderon and Mullen [1].

Original languageEnglish (US)
Pages (from-to)917-931
Number of pages15
JournalTaiwanese Journal of Mathematics
Volume12
Issue number4
DOIs
StatePublished - Jul 2008

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'On the number of solutions of equations of Dickson polynomials over finite fields'. Together they form a unique fingerprint.

Cite this