The most widely known result of Chevalley–Warning type states that if one has a polynomial over a finite field of characteristic p, and the number of variables exceeds the degree, then the number of zeros is a multiple of p. In particular, if the polynomial is homogeneous, there is at least one non-trivial zero. There are a number of related results in the literature. Generally, let Fq be a finite field, and let f = (f1(x), . . . , fr(x)) be an r-tuple of polynomials fi(x1, . . . , xn) ∈ Fq[x1… CONTINUE READING