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Is there a polynomial in $ \Bbb Z[x]$ such that for every $ n\in\{0,1,\dots,2^m\}$ we have $ $ n\equiv2\bmod4\implies f(n)\equiv0\bmod 2$ $ $ $ n\equiv0\bmod4\implies f(n)\equiv1\bmod 2$ $ and can the coefficients be bound by $ 2^{O(poly(m))}$ and degree bound by $ O(poly(m))$ ?Read more