Given a prime power $q$ and an integer $n\geq2$, we establish a sufficient condition for the existence of a primitive pair $(\alpha,f(\alpha))$ where $\alpha \in \mathbb{F}_q$ and $f(x) \in \mathbb{F}_q(x)$ is a rational function of degree $n$. (Here $f=f_1/f_2$, where $f_1, f_2$ are coprime polynomials of degree $n_1,n_2$, respectively, and $n_1+n_2=n$.).. (read more)

PDF- NUMBER THEORY

- COMMUTATIVE ALGEBRA