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Claim. R. de la Bretèche, Plus grand facteur premier de valeurs de polynômes aux entiers, Acta Arith. 169 (2015), 221--250, proves that for every even monic irreducible quartic $f\in\mathbb Z[X]$ whose Galois group is isomorphic to the Klein group $V_4=\mathbb Z/2\mathbb Z\times\mathbb Z/2\mathbb Z$ there is $c>0$ such that the integers $n\le X$ with $P^+(f(n))>X^{1+c}$ have positive density. Hence $F_f(X)>X^{1+c}$ for all large $X$, in the notation of Problem 976. The result extends Dartyge's 2015 theorem for $X^4-X^2+1$, as the introduction of Dartyge and Maynard's paper on cyclic and dihedral quartics records.

Covers. The first question for even monic irreducible quartics with Galois group $V_4$. It does not give $F_f(n)\gg n^4$.

Depends on. No page of this wiki.

Acceptance. Refereed: Acta Arithmetica 169 (2015), no. 3, 221--250, published online on 22 June 2015. The site labels the problem OPEN.