Distinct coordinate solutions of linear equations over finite fields

Jiyou Li, Xiang Yu

Let ${\mathbb{F}}_q$ be the finite field of $q$ elements and $a_1,a_2,\dots ,a_k,b\in {\mathbb{F}}_q$. We investigate $N_{{\mathbb{F}}_q}(a_1,a_2,\dots ,a_k;b)$, the number of order…