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BALTIC-WAY 2019 Problem 20

    Let us consider a polynomial P(x)P(x) with integers coefficients satisfying P(−1)=−4, P(−3)=−40, and P(−5)=−156.P(-1)=-4,\ P(-3)=-40,\text{ and } P(-5)=-156. What is the largest possible number of integers xx satisfying P(P(x))=x2?P(P(x))=x^2?

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