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arXiv · 2606.02244

On the unit equation $\varepsilon+\delta=n$ in cubic fields

Maleeha Khawaja·Samir Siksek
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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.

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Maleeha Khawaja, Samir Siksek. 2026-06-01. On the unit equation $\varepsilon+\delta=n$ in cubic fields. https://arxiv.org/abs/2606.02244

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