5 papers
Consecutive non-square non-primitive tuples in finite fields
Juncheng Zhou, Hongfeng Wu
Let be an odd prime power and put \[ θ_q=\frac{φ(q-1)}{q-1}. \] An element of $\Fq$ is called non-square non-primitive, or \emph{NSNP}, if it is both a non-square and a non-pri…
Primitive Quadratic Polynomials in Additive Coset Families
Juncheng Zhou, Hongfeng Wu
Let \(q\) be an odd prime power. For \(μ\in\mathbb F_q^\times\) and an additive coset \(\barα\in\mathbb F_{q^2}/\mathbb F_q\), consider the family \[ \{x^2+μx-α:α\in\barα\}, \] whe…
Finite fields whose members are the sum of a potent and a 5-potent
Juncheng Zhou, Peter V. Danchev, Hongfeng Wu
We show that there are only finitely many finite fields whose members are the sum of an -potent element and a -potent element. Combining this with the algorithmic results pro…
Cyclotomy, cyclotomic cosets and arithmetic properties of some families in
Juncheng Zhou, Hongfeng Wu
Arithmetic properties of some families in are obtained by using the cyclotomic classes of order 2 with respect to ,…
The Multiple Equal-Difference Structure of Cyclotomic Cosets
Li Zhu, Juncheng Zhou, Jinle Liu +1
In this paper we introduce the definition of equal-difference cyclotomic coset, and prove that in general any cyclotomic coset can be decomposed into a disjoint union of equal-diff…