Displaying similar documents to “Sur les décompositions des nombres naturels en sommes de nombres premiers”

Remarques sur le premier cas du théorème de Fermat sur les corps de nombres

Alain Kraus (2015)

Acta Arithmetica

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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 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...