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On the largest prime factor of quartic polynomial values: the cyclic and dihedral cases
Published 7 Dec 2022 in math.NT | (2212.03381v1)
Abstract: Let $P(X)\in\mathbb{Z}[X]$ be an irreducible, monic, quartic polynomial with cyclic or dihedral Galois group. We prove that there exists a constant $c_P>0$ such that for a positive proportion of integers $n$, $P(n)$ has a prime factor $\ge n{1+c_P}$.
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