A bound on the number of points of a curve in projective space over a finite field

For a nondegenerate irreducible curve $C$ of degree $d$ in ${\mathbb{P}}^r$ over ${\mathbb{F}}_q$ with $r\ge 3$, we prove that the number $N_q(C)$ of ${\Bbb F}_q$-pointsof$C$satisfiestheinequality$N_q© \leq (d-1)q +1$, which is known as Sziklai’s bound if $r=2$.