MathDB
2020 Team #10

Source:

October 24, 2023
team test

Problem Statement

Let r=1−25+45−85+165r = 1-\sqrt[5]{2}+ \sqrt[5]{4}-\sqrt[5]{8}+ \sqrt[5]{16}. There exists a unique fifth-degree polynomial PP such that its leading coefficient is positive, all of its coefficients are integers whose greatest common factor (among all of them) is 11, and P(r)=0P(r) = 0. Evaluate P(10)P(10).
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