# MathSciDoc: An Archive for Mathematician ∫

#### Number Theorymathscidoc:1701.24004

Acta Mathematica, 213, (1), 107-135, 2012.6
Let $${f \in \mathbb{Z}[x]}$$ , $${\deg f =3}$$ . Assume that$f$does not have repeated roots. Assume as well that, for every prime$q$, $${f(x)\not\equiv 0}$$ mod$q$^{2}has at least one solution in $${(\mathbb{Z}/q^2 \mathbb{Z})^*}$$ . Then, under these two necessary conditions, there are infinitely many primes$p$such that$f$($p$) is square-free.
@inproceedings{harald2012square-free,
title={Square-free values of$f$($p$),$f$cubic},
author={Harald Andrés Helfgott},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203403406610793},
booktitle={Acta Mathematica},
volume={213},
number={1},
pages={107-135},
year={2012},
}

Harald Andrés Helfgott. Square-free values of$f$($p$),$f$cubic. 2012. Vol. 213. In Acta Mathematica. pp.107-135. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203403406610793.