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arXiv · 2512.04936

A survey on the generalized Fermat equation of various signatures over totally real fields

Satyabrat Sahoo
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Abstract

Following the famous proof of Fermat's Last Theorem by Andrew Wiles using the modularity of elliptic curves over $\mathbb{Q}$, significant developments have been made in the study of Diophantine equations using the modularity method. This article presents a survey of numerous results on the solutions of the generalized Fermat equation of signatures $(p,p,p)$, $(p,p,2)$, $(p,p,3)$, and $(r,r,p)$ over totally real number fields using the modularity method.

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Satyabrat Sahoo. 2025-12-04. A survey on the generalized Fermat equation of various signatures over totally real fields. https://arxiv.org/abs/2512.04936

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