9 citations · 9 across the 5 of their papers we have counts for
7 papers · 1 filter
On Permutation Trinomials and Complete Permutation Polynomials via Fiber Criteria over Finite Fields
Chahrazade Bouyacoub, Asmae El-Baz, Omar Kihel
We give new, short proofs of recent permutation polynomial results of Bousalmi, Bayad, and Derbal by reducing the verification to explicit computations on a three-element multiplic…
When is the ring of integers of a number field coverable?
Mohamed Ayad, Omar Kihel
A commutative ring R is said to be coverable if it is the union of its proper subrings and said to be finitely coverable if it is the union of a finite number of them. In the latte…
Prime rational functions over a field
Eva Goedhart, Omar Kihel, Jesse Larone
The aim of this paper is to provide sufficient conditions for when a polynomial or rational function over a field K is prime using its order of vanishing at infinity and the result…
The paradox of the infinity
Mohamed Ayad, Omar Kihel
\textit{Let be an infinite set on which a property is defined. Suppose that is a partition, where each is infinite. Suppose also that, in…
Proof of the conjecture of Keskin, Siar and Karaatli
Rachid Boumahdi, Omar Kihel, Sukrawan Mavecha
In this paper among other results, we will prove the conjecture of Keskin, Siar and Karaatli on the Diophantine equation .
The number of solutions to
Tarek Garici, Omar Kihel, Jesse Larone
In this paper, we find a bound for the number of the positive solutions to the titled equation, improving a result of Togbé. As a consequence, we prove a conjecture of Togbé in a f…
On Permutation Binomials over Finite Fields
Mohamed Ayad, Belghaba Kacem, Omar Kihel
Let be the finite field of characteristic containing elements and a binomial with coefficients in this field. If some conditi…