The equation x 2n +y 2n =z 5
Journal de théorie des nombres de Bordeaux, Volume 18 (2006) no. 2, pp. 315-321.

We show that the Diophantine equation of the title has, for n>1, no solution in coprime nonzero integers x,y and z. 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 x,y,z, telles que (x,y)=(y,z)=(x,z)=1 et xyz0. La démonstration utilise les courbes de Frey et des résultats liés à la modularité des représentations galoisiennes.

DOI: 10.5802/jtnb.546
Bennett, Michael A. 1

1 University of British Columbia 1984 Mathematics Road Vancouver, B.C. Canada
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Bennett, Michael A. The equation $x^{2n}+y^{2n}=z^5$. Journal de théorie des nombres de Bordeaux, Volume 18 (2006) no. 2, pp. 315-321. doi : 10.5802/jtnb.546. http://www.numdam.org/articles/10.5802/jtnb.546/

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