Square-free values of$f$($p$),$f$cubic

Harald Andrés Helfgott Département de Mathématiques, École Normale Supérieure

Number Theory mathscidoc: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.
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@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.
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