Mathematics > Number Theory
arXiv:2606.02244 (math)
[Submitted on 1 Jun 2026 (v1), last revised 2 Jun 2026 (this version, v2)]
Abstract:Let $n$ be an integer not equal to $-2$, $0$ or $2$. We consider the unit equation $\varepsilon + \delta = n$ in units $\varepsilon, \delta$ of cubic fields. We show that this equation has no solutions for 100% of cubic fields, when ordered by discriminant. This is consistent with a recent conjecture of the authors.
Submission history
From: Maleeha Khawaja [view email]
[v1]
Mon, 1 Jun 2026 13:39:18 UTC (11 KB)
[v2]
Tue, 2 Jun 2026 13:15:23 UTC (11 KB)
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