12 citations · 38 across the 20 of their papers we have counts for
23 papers
Triples and quadruples of consecutive squares or non-squares in a finite field
Stephen D. Cohen
Let $\F$ be the finite field of odd prime power order , We find explicit expressions for the number of triples $\{\al-1,\al,\al+1 \}$ of consecutive non-zero squares in $\F$ and…
Primitive element pairs with a prescribed trace in the cubic extension of a finite field
Andrew R. Booker, Stephen D. Cohen, Nicol Leong +1
We prove that for any prime power , the cubic extension of the finite field contains a primitive element such that $ξ+ξ^{-1}…
Rings and finite fields whose elements are sums or differences of tripotents and potents
Adel N. Abyzov, Stephen D. Cohen, Peter V. Danchev +1
We significantly strengthen results on the structure of matrix rings over finite fields and apply them to describe the structure of the so-called weakly -torsion clean rings. Sp…
Primitive elements with prescribed traces
Andrew R. Booker, Stephen D. Cohen, Nicol Leong +1
Given a prime power and a positive integer , let denote the finite field with elements. Also let be arbitrary members of the ground field $\…
Four consecutive primitive elements in a finite field
Tamiru Jarso, Tim Trudgian
For an odd prime power, we prove that there are always four consecutive primitive elements in the finite field when .
The trace of primitive and -primitive elements in finite fields, revisited
Stephen D. Cohen, Giorgos Kapetanakis
By definition primitive and -primitive elements of a finite field extension have order and , respectively. We have already shown that, with…