Modular congruences, Q-curves, and the diophantine equation $x^4 + y^4 = z^p $

Dieulefait, Luis V.

Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, p. 363-369 / Harvested from Project Euclid

Résumé

We prove two results concerning the generalized Fermat equation $x^4 + y^4 = z^p$. In particular we prove that the First Case is true if $p \neq 7$

Publié le : 2005-09-14
Classification: diophantine equations, elliptic curves, modular forms, 11D41, 11F11

@article{1126195341,
     author = {Dieulefait, Luis V.},
     title = {Modular congruences, Q-curves, and the diophantine equation $x^4 + y^4 = z^p $},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {11},
     number = {5},
     year = {2005},
     pages = { 363-369},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1126195341}
}

Dieulefait, Luis V. Modular congruences, Q-curves, and the diophantine equation $x^4 + y^4 = z^p $. Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2005) no. 5, pp.  363-369. http://gdmltest.u-ga.fr/item/1126195341/