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Z[x], P(\sqrt[3]5+\sqrt[3]25)=5+\sqrt[3]5

Source: VJIMC 2013 2.3

May 31, 2021
algebranumber theoryPolynomials

Problem Statement

Prove that there is no polynomial PP with integer coefficients such that P(53+253)=5+53P\left(\sqrt[3]5+\sqrt[3]{25}\right)=5+\sqrt[3]5.
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