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Possible values of P(2005)

Source: Finnish Mathematics Competition 2010, Final Round, Problem 3

November 15, 2011
algebrapolynomialalgebra unsolved

Problem Statement

Let P(x)P(x) be a polynomial with integer coefficients and roots 19971997 and 20102010. Suppose further that ∣P(2005)∣<10|P(2005)|<10. Determine what integer values P(2005)P(2005) can get.
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