Counting squarefree discriminants of trinomials under abc

Details Counting squarefree discriminants of trinomials under abc Counting squarefree discriminants of trinomials under abc

2008-08-04

arxiv.org/abs/0808.0418v1

Mathematics

Number Theory

9 Pages

Scientific paper

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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