Counting squarefree discriminants of trinomials under abc

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.

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Cited by in corpus (1)

• On Quadratic Fields Generated by Discriminants of Irreducible Trinomials