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Problem 8 of First round

Source: I International Festival of Young Mathematicians Sozopol 2010, Theme for 10-12 grade

December 13, 2019
algebrapolynomial

Problem Statement

Find all polynomials f(x)f(x) with integer coefficients and leading coefficient equal to 1, for which f(0)=2010f(0)=2010 and for each irrational xx, f(x)f(x) is also irrational.
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