On the Chevalley-Warning Theorem When the Degree Equals the Number of Variables

Hector Pasten

Abstract: Let f be a degree d polynomial in n variables defined over a finite field k of characteristic p and let N be the number of zeros of f in kn. The Chevalley-Warning theorem asserts that if d<n, then N is divisible by p. In this note we show a version of the result for d = n.