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Last edited by hbghlyj at 2023-1-23 20:33:00 Suppose that $p ∈ ℚ[X]$ maps integers to integers and is such that for all $z∈ℤ$ either 2 divides $p(z)$ or 3 divides $p(z)$. Show that the quantifiers may be reversed i.e. that either for all $z∈ℤ$ we have 2 divides $p(z)$, or for all $z∈ℤ$ we have 3 divides $p(z)$. 设 $p ∈ ℚ[X]$ 将整数映射到整数，并且对于所有 $z∈ℤ$，$p(z)$ 是 2 或 3 的倍数。证明对于所有 $z∈ℤ$ 我们有 $p(z)$ 是 2 的倍数，或者对于所有 $z∈ℤ$ 我们有 $p(z)$ 是 3 的倍数。 | 
