Combinatorial Nullstellensatz
= Combinatorial Nullstellensatz
{c}
{wiki}
One coefficient form of the Combinatorial Nullstellensatz says that if $\deg f\leq d_1+\cdots+d_n$ and $[x_1^{d_1}\cdots x_n^{d_n}]f\ne0$, then for every choice of sets $A_i$ with $|A_i|=d_i+1$ there is a point $(a_1,\ldots,a_n)\in A_1\times\cdots\times A_n$ at which $f$ does not vanish.