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This is a Quantitative Study study.

September 23, 2025Open Access

On Fermat's Last Theorem over the Z₃-extension of Q and other fields

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Proof of Fermat's Last Theorem established for large prime exponents, with those primes equivalent to 2 mod 3.
The findings are applicable within maximal real subfields of cyclotomic extensions, particularly at varying n values.
A novel approach combines the modular method with a generalization of Pomey's arithmetic result for these specific fields.
Potential implications include broader applications of arithmetic techniques in number theory and algebraic structures.

Implication

This article demonstrates Fermat's Last Theorem over number fields, suggesting expanded applicability of modular methods.

Abstract

The main result of the present article is a proof of Fermat's Last Theorem for sufficiently large prime exponents p with p ≡ 2 3 over certain number fields. A particular case of these fields are the maximal real subfields of the cyclotomic extensions Q(ζ3ⁿ) for every n. Our strategy consists in combining the modular method with a generalization of an arithmetic result of Pomey to these fields.

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Cite This Study

Dieulefait et al. (2025) studied this question.

synapsesocial.com/papers/68d4759931b076d99fa6db7a https://doi.org/10.48550/arxiv.2507.16883

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Implication

This article demonstrates Fermat's Last Theorem over number fields, suggesting expanded applicability of modular methods.

On Fermat's Last Theorem over the Z₃-extension of Q and other fields

Key Points

Implication

Abstract

Discussion

Cite This Study

On Fermat's Last Theorem over the Z₃-extension of Q and other fields

Key Points

Implication

Abstract

Discussion

Cite This Study

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