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MathNet 2019-part-01 — 184 problems (EN–VI) Question 61

Math Olympiad Vault · MathNet 2019-part-01 — 184 problems (EN–VI)

Question 61

Does there exist a polynomial $f(x)$ with integer coefficients of degree four such that for any integer $k$, the polynomial $f(x) + k$ is either irreducible or has a rational root?