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