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

• Autorzy: Alain Kraus
• Języki publikacji: FR EN

Abstrakty

EN

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 a well known statement over ℚ, we give an easily testable condition which allows one occasionally to prove the first case of Fermat's Last Theorem over number fields for a prime number p ≡ 2 (mod 3).

Kategorie tematyczne

• 11D41: Higher degree equations; Fermat's equation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 167
• Numer: 2
• Strony: 133-141

Daty

wydano

2015

Twórcy

autor

Alain Kraus

• Équipe de Théorie des Nombres, Institut de Mathématiques de Jussieu, Université de Paris VI, 4 Place Jussieu, 75005 Paris, France

Identyfikatory

DOI

10.4064/aa167-2-3