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arXiv · 2003.05791

Chevalley's class number formula, unit equations and the asymptotic Fermat's Last Theorem

Nuno Freitas·Alain Kraus·Samir Siksek
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Abstract

Let $F$ be a number field and $\mathcal{O}_F$ its ring of integers. We use Chevalley's ambiguous class number formula to give a criterion for the non-existence of solutions to the unit equation $λ+ μ= 1$, $λ, μ\in \mathcal{O}_F^\times$. This is then used to strengthen a criterion for the asymptotic Fermat's Last Theorem due to Freitas and Siksek.

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Nuno Freitas, Alain Kraus, Samir Siksek. 2020-03-15. Chevalley's class number formula, unit equations and the asymptotic Fermat's Last Theorem. https://arxiv.org/abs/2003.05791

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