### Abstract

Let k, n_{1}, ..., n_{k} be fixed positive integers, c_{1}, ..., c_{k} ∈ GF(q)*, and a_{1}, ..., a_{k}, c ∈ GF(q). We study the number of solutions in GF(q) of the equation c_{1}D_{n1}(x_{1}, a_{1})+c_{2}D_{n2}(x_{2}, a_{2})+...+c_{k}D_{nk}(x_{k}, a_{k}) = c, where each D_{ni}(x_{i}, a_{i}), 1 ≤ i ≤ k, is the Dickson polynomial of degree n_{i} with parameter a_{i}. 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 language | English (US) |
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Pages (from-to) | 917-931 |

Number of pages | 15 |

Journal | Taiwanese Journal of Mathematics |

Volume | 12 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 2008 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Taiwanese Journal of Mathematics*,

*12*(4), 917-931. https://doi.org/10.11650/twjm/1500404986

}

*Taiwanese Journal of Mathematics*, vol. 12, no. 4, pp. 917-931. https://doi.org/10.11650/twjm/1500404986

**On the number of solutions of equations of Dickson polynomials over finite fields.** / Chou, Wun Seng; Mullen, Gary Lee; Wassermann, Bertram.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the number of solutions of equations of Dickson polynomials over finite fields

AU - Chou, Wun Seng

AU - Mullen, Gary Lee

AU - Wassermann, Bertram

PY - 2008/1/1

Y1 - 2008/1/1

N2 - 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].

AB - 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].

UR - http://www.scopus.com/inward/record.url?scp=77952150487&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77952150487&partnerID=8YFLogxK

U2 - 10.11650/twjm/1500404986

DO - 10.11650/twjm/1500404986

M3 - Article

AN - SCOPUS:77952150487

VL - 12

SP - 917

EP - 931

JO - Taiwanese Journal of Mathematics

JF - Taiwanese Journal of Mathematics

SN - 1027-5487

IS - 4

ER -