MathDB
Lowest degree of polynomial

Source: 2021 Korea Winter Program Test2 Day1 #4

February 7, 2021
number theoryInteger Polynomial

Problem Statement

Find all f(x)∈Z(x)f(x)\in \mathbb Z (x) that satisfies the following condition, with the lowest degree. Condition: There exists g(x),h(x)∈Z(x)g(x),h(x)\in \mathbb Z (x) such that f(x)4+2f(x)+2=(x4+2x2+2)g(x)+3h(x)f(x)^4+2f(x)+2=(x^4+2x^2+2)g(x)+3h(x).
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