Counting squarefree discriminants of trinomials under abc

Anirban Mukhopadhyay; M. Ram Murty; Kotyada Srinivas

Counting squarefree discriminants of trinomials under abc

Number Theory 2008-08-05 v1

Authors: Anirban Mukhopadhyay , M. Ram Murty , Kotyada Srinivas

Abstract

For an odd positive integer $n\ge 5$ , assuming the truth of the $abc$ conjecture, we show that for a positive proportion of pairs $(a,b)$ of integers the trinomials of the form $t^n+at+b (a,b\in \mathbb Z)$ are irreducible and their discriminants are squarefree.

Keywords

abc conjecture trinomials squarefree discriminants irreducibility number theory

Cite

@article{arxiv.0808.0418,
  title  = {Counting squarefree discriminants of trinomials under abc},
  author = {Anirban Mukhopadhyay and M. Ram Murty and Kotyada Srinivas},
  journal= {arXiv preprint arXiv:0808.0418},
  year   = {2008}
}

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