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integer P(x) with roots \sqrt2 + \sqrt3 and \sqrt2 + \sqrt[3]{3}

Source: 1964 Swedish Mathematical Competition p3

March 21, 2021
radicalInteger Polynomialpolynomialalgebra

Problem Statement

Find a polynomial with integer coefficients which has 2+3\sqrt2 + \sqrt3 and 2+33\sqrt2 + \sqrt[3]{3} as roots.