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- W4300650241 abstract "The first case of Fermat's Last Theorem for a prime exponent $p$ can sometimes be proved using the existence of local obstructions. In 1823, Sophie Germain has obtained an important result in this direction by establishing that, if $2p+1$ is a prime number, the first case of Fermat's Last Theorem is true for $p$. In this paper, we investigate such obstructions over number fields. We obtain analogous results on Sophie Germain type criteria, for imaginary quadratic fields. Furthermore, extending a well known statement over ${bf Q}$, we give an easily testable condition which allows occasionally to prove the first case of Fermat's Last Theorem over number fields for a prime number $pequiv 2 mod 3$." @default.
- W4300650241 created "2022-10-03" @default.
- W4300650241 creator A5042297370 @default.
- W4300650241 date "2014-10-02" @default.
- W4300650241 modified "2023-10-18" @default.
- W4300650241 title "Remarques sur le premier cas du th'eor`eme de Fermat sur les corps de nombres" @default.
- W4300650241 doi "https://doi.org/10.48550/arxiv.1410.0546" @default.
- W4300650241 hasPublicationYear "2014" @default.
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