ArticleOriginal scientific text

Title

Some diophantine equations of the form xn+yn=zm

Authors 1

Affiliations

  1. Department of Mathematics, University of California, Berkeley, California 94720-3840, U.S.A.

Keywords

generalized Fermat equation, diophantine equations, descent

Bibliography

  1. [Be] F. Beukers, The Diophantine equation Axp+Byq=Czr, Duke Math. J. 91 (1998), no. 1, 61-88.
  2. [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.
  3. [Cr] J. E. Cremona, Algorithms for Modular Elliptic Curves, Cambridge Univ. Press, 1992.
  4. [DM] H. Darmon and L. Merel, Winding quotients and some variants of Fermat's Last Theorem, J. Reine Angew. Math. 490 (1997), 81-100.
  5. [De] P. Dénes, Über die Diophantische Gleichung xl+yl=czl, Acta Math. 88 (1952), 241-251.
  6. [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.
  7. [Sc] E. F. Schaefer, Computing a Selmer group of a Jacobian using functions on the curve, Math. Ann. 310 (1998), 447-471.
Pages:
193-205
Main language of publication
English
Received
1997-03-04
Published
1998
Exact and natural sciences