Problem

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Tags: number theory



Let $P(x) = 2x^3-3x^2+2$, and the sets: $$A =\{ P(n) | n \in N, n \le 1999\}, B=\{p^2+1 |p \in N\}, C=\{ q^2+2 | q \in N\}$$Prove that the sets $A \cap B$ and $A\cap C$ have the same number of elements