Some diophantine equations of the form x n + y n = z m

Bjorn Poonen

Acta Arithmetica (1998)

  • Volume: 86, Issue: 3, page 193-205
  • ISSN: 0065-1036

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Bjorn Poonen. "Some diophantine equations of the form $x^n + y^n = z^m$." Acta Arithmetica 86.3 (1998): 193-205. <http://eudml.org/doc/207189>.

@article{BjornPoonen1998,
author = {Bjorn Poonen},
journal = {Acta Arithmetica},
keywords = {generalized Fermat equation; diophantine equations; descent; higher degree diophantine equations; elliptic curves},
language = {eng},
number = {3},
pages = {193-205},
title = {Some diophantine equations of the form $x^n + y^n = z^m$},
url = {http://eudml.org/doc/207189},
volume = {86},
year = {1998},
}

TY - JOUR
AU - Bjorn Poonen
TI - Some diophantine equations of the form $x^n + y^n = z^m$
JO - Acta Arithmetica
PY - 1998
VL - 86
IS - 3
SP - 193
EP - 205
LA - eng
KW - generalized Fermat equation; diophantine equations; descent; higher degree diophantine equations; elliptic curves
UR - http://eudml.org/doc/207189
ER -

References

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  1. [Be] F. Beukers, The Diophantine equation A x p + B y q = C z r , 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. Zbl0758.14042
  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. Zbl0976.11017
  5. [De] P. Dénes, Über die Diophantische Gleichung x l + y l = c z l , Acta Math. 88 (1952), 241-251. Zbl0048.27503
  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. Zbl0888.11023
  7. [Sc] E. F. Schaefer, Computing a Selmer group of a Jacobian using functions on the curve, Math. Ann. 310 (1998), 447-471. Zbl0889.11021

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