# nt.quantity principle – On variety of monomials in inescapable constrained polynomials Answer

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## nt.quantity principle – On variety of monomials in inescapable constrained polynomials

At each $$nin{1,2,dots,}$$ and at each $$qinmathcal I={2,3,dots,p}$$ is there a polynomial $$g_q$$ the place $$mathcal I$$ is a clique of primes and $$p=O(1)$$ having variety of monomials $${poly(n)}$$ satisfying the circumstances

1. $$Big(oplus_{qinmathcal I}mathbb 1_{g_q(x_1,dots,x_n)bmod q}Big)equiv1iff2sum_{i=1}^nx_igeq n$$
at each $$(x_1,dots,x_n)in{0,1}^n$$ the place $$mathbb 1_a=1iff a=0$$ and the place $$oplus$$ is $$bmod 2$$

2. $$g_q(x_1,dots,x_n)inmathbb Z[x_1,dots,x_n]$$

3. each coefficient of $$g_q$$ has magnitude sure by $$2^{poly(n)}$$

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