2 papers
math.NT2026
Necessary and sufficient conditions on the order of a finite field for the easy identification of primitive polynomials of degree 2
Gerardo Vega
We present the necessary and sufficient conditions on the order of a finite field such that every irreducible polynomial of the form $x^2+bx+c \in \mathbb{F}_q[x…
math.GM2024
A characterization and an explicit description of all primitive polynomials of degree two over finite fields
Gerardo Vega
For polynomials of degree two over finite fields, we present an improvement of Fitzgerald's characterization (Finite Fields Appl. 9(1):117-121, 2003). We then use this new characte…