January 31, 2025Open Access

On the largest prime factor of quartic polynomial values: the cyclic and dihedral cases

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Abstract

Let P (X) X be an irreducible, monic, quartic polynomial with cyclic or dihedral Galois group. We prove that there exists a constant c₏>0 such that for a positive proportion of integers n, P (n) has a prime factor n^1+cP.

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Dartyge et al. (Fri,) studied this question.

synapsesocial.com/papers/68e55b5ae2b3180350ef8b3d https://doi.org/https://doi.org/10.4171/jems/1586

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