We show that the Diophantine equation of the title has, for , no solution in coprime nonzero integers and . Our proof relies upon Frey curves and related results on the modularity of Galois representations.
Nous montrons que l’équation diophantienne ci-dessus n’admet pas de solutions entières , telles que et . La démonstration utilise les courbes de Frey et des résultats liés à la modularité des représentations galoisiennes.
Publié le :
DOI : 10.5802/jtnb.546
Michael A. Bennett 1
Michael A. Bennett. The equation $x^{2n}+y^{2n}=z^5$. Journal de théorie des nombres de Bordeaux, Tome 18 (2006) no. 2, pp. 315-321. doi: 10.5802/jtnb.546
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pages = {315--321},
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publisher = {Universit\'e Bordeaux 1},
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