A Polynomial Through Two Surds

Problem

A degree- $4$ integer-coefficient polynomial $f$ satisfies

f\left(1 + \sqrt[3]{3}\right) = 1 + \sqrt[3]{3}, \qquad f\left(1 + \sqrt3\right) = 7 + \sqrt3.

Find $f(x)$ .

Answer

Solution

Difficulty	8/10
Topics	number theory, algebra, Polynomials

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