# Some diophantine equations of the form ${x}^{n}+{y}^{n}={z}^{m}$

Acta Arithmetica (1998)

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

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top## How to cite

topBjorn 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

top- [Be] F. Beukers, The Diophantine equation $A{x}^{p}+B{y}^{q}=C{z}^{r}$, Duke Math. J. 91 (1998), no. 1, 61-88.
- [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.
- [Cr] J. E. Cremona, Algorithms for Modular Elliptic Curves, Cambridge Univ. Press, 1992. Zbl0758.14042
- [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
- [De] P. Dénes, Über die Diophantische Gleichung ${x}^{l}+{y}^{l}=c{z}^{l}$, Acta Math. 88 (1952), 241-251. Zbl0048.27503
- [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
- [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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