$F$-Diophantine sets over finite fields
$F$-Diophantine sets over finite fields
Let $k \geq 2$, $q$ be an odd prime power, and $F \in \mathbb{F}_q[x_1, \ldots, x_k]$ be a polynomial. An $F$-Diophantine set over a finite field $\mathbb{F}_q$ is a set $A \subset \mathbb{F}_q^*$ such that $F(a_1, a_2, \ldots, a_k)$ is a square in $\mathbb{F}_q$ whenever $a_1, a_2, \ldots, a_k$ are …