Davenport Pairs over Finite Fields
Wayne Aitken, Michael D. Fried, and Linda M. Holt
A pair of polynomials $f,g \in {\mathbb F}_q[T]$ is called a Davenport pair if their value sets are equal, ${\mathbb V}_f({\mathbb F}_{q^t})= {\mathbb V}_g({\mathbb F}_{q^t})$, for infinitely many extensions of ${\mathbb F}_q$. This paper studies such pairs.