Counting squarefree discriminants of trinomials under abc

Mukhopadhyay, Anirban; Murty, M.; Srinivas, Kotyada

doi:10.1090/S0002-9939-09-09831-1

Counting squarefree discriminants of trinomials under abc
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by Anirban Mukhopadhyay, M. Ram Murty and Kotyada Srinivas PDF

Proc. Amer. Math. Soc. 137 (2009), 3219-3226 Request permission

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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