  Let $\mathbb F_q$ denote the finite field with $q$ elements. In this paper we
use the relationship between suitable polynomials and number of rational points
on algebraic curves to give the exact number of elements $a\in \mathbb F_q$ for
which the binomial $x^n(x^{(q-1)/r} + a)$ is a permutation polynomial in the
cases $r = 2$ and $r = 3$.
