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arXiv · 0808.0418

Counting squarefree discriminants of trinomials under abc

Anirban Mukhopadhyay·M. Ram Murty·Kotyada Srinivas
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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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Anirban Mukhopadhyay, M. Ram Murty, Kotyada Srinivas. 2008-08-04. Counting squarefree discriminants of trinomials under abc. https://arxiv.org/abs/0808.0418

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