This paper was removed due to an error in the proof (Claim 4.12 as stated is not true). The authors would like to thank Ilya Volkovich for pointing out a counterexample to this papers main result in positive characteristic: If $F$ is a field with prime characteristic $p$, then the polynomial $x_1^p + x_2^p + ldots + x^n^p$ has the following factor: $(x_1+x_2+ ldots + x_n)^{p-1}$, which has sparsity $n^p$.
Download