Some diophantine equations of the form xn+yn=zm
Bjorn Poonen
Acta Arithmetica, Tome 84 (1998), p. 193-205 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)
Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:207189 
@article{bwmeta1.element.bwnjournal-article-aav86i3p193bwm,
     author = {Bjorn Poonen},
     title = {Some diophantine equations of the form $x^n + y^n = z^m$
            },
     journal = {Acta Arithmetica},
     volume = {84},
     year = {1998},
     pages = {193-205},
     zbl = {0930.11017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav86i3p193bwm}
}

Bjorn Poonen. Some diophantine equations of the form $x^n + y^n = z^m$
            . Acta Arithmetica, Tome 84 (1998) pp. 193-205. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav86i3p193bwm/

[000] [Be] F. Beukers, The Diophantine equation Axp+Byq=Czr, Duke Math. J. 91 (1998), no. 1, 61-88.

[001] [Ca] J. W. S. Cassels, The Mordell-Weil group of curves of genus 2, in: Arithmetic and Geometry, Vol. I, Progr. Math. 35, Birkhäuser, Boston, Mass., 1983, 27-60.

[002] [Cr] J. E. Cremona, Algorithms for Modular Elliptic Curves, Cambridge Univ. Press, 1992. | Zbl 0758.14042

[003] [DM] H. Darmon and L. Merel, Winding quotients and some variants of Fermat's Last Theorem, J. Reine Angew. Math. 490 (1997), 81-100. | Zbl 0976.11017

[004] [De] P. Dénes, Über die Diophantische Gleichung xl+yl=czl, Acta Math. 88 (1952), 241-251. | Zbl 0048.27503

[005] [PS] B. Poonen and E. F. Schaefer, Explicit descent for Jacobians of cyclic covers of the projective line, J. Reine Angew. Math. 488 (1997), 141-188. | Zbl 0888.11023

[006] [Sc] E. F. Schaefer, Computing a Selmer group of a Jacobian using functions on the curve, Math. Ann. 310 (1998), 447-471. | Zbl 0889.11021