Chevalley's theorem, also known as the Chevalley-Waring theorem, states that if 
is a polynomial in ![F[x_1,...,x_n]](/images/equations/ChevalleysTheorem/Inline2.svg)
, where 
is a finite field of field
characteristic 
,
and the degree of 
is less than 
,
then the number of zeros of 
in 
is equal to 0 (mod 
).
In the special case that 
is a homogeneous polynomial, the theorem states that if 
and 
is greater than the degree of 
, then 
has at least two zeros in 
.
