Estimating the Number Of Roots of Trinomials over Finite Fields

Zander Kelley, Sean Owen

We show that univariate trinomials $x^n+a{x}^s+b\in {\mathbb{F}}_q[x]$ can have at most $\delta \lfloor \frac{1}{2}+\sqrt{\frac{q-1}{\delta }}\rfloor$ distinct roots in ${\mathbb{F}}_q$…