Chevalley's Theorem

Let $f(x)$ be a member of a Finite Field $F[x_1, x_2, \ldots, x_n]$ and suppose $f(0,0,\ldots,0)=0$ and $n$ is greater than the degree of $f$, then $f$ has at least two zeros in $A^n(F)$.

References

Chevalley, C. ``Démonstration d'une hypothèse de M. Artin.'' Abhand. Math. Sem. Hamburg 11, 73-75, 1936.

Ireland, K. and Rosen, M. ``Chevalley's Theorem.'' §10.2 in A Classical Introduction to Modern Number Theory, 2nd ed. New York: Springer-Verlag, pp. 143-144, 1990.