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$\DeclareMathOperator\bias{bias}$I'm trying to figure out how to approach the following question: Let $g$, $h$ be polynomials over $\mathbb{Z}_p$ (for prime $p$) with $n>1$ variables. Denote by $\...

At every $n\in\mathbb N$ (all polynomials are of degree $O(1)$) is there $g_{3,1}^{(n)},\dots,g_{3,k}^{(n)}\in\mathbb F_3[x_1,\dots,x_n]$ at $k=\mathsf{poly}(n)$ and $g_2^{(n)}\in\mathbb F_2[x_1,\dots,...