On fermat’s quadruple equations

  • Emanuel Herrmann
  • Attila Pethő
  • Horst G. Zimmer


Elliptic Curve Elliptic Curf Rational Solution Diophantine Equation Acta Arith 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. Coates, An effective p-adic analogue of a theorem of Thue III: The diophantine equation y2 = x3 + k.Acta Arith. 74 (1970), 425–435.MathSciNetGoogle Scholar
  2. [2]
    A. Dujella, Generalization of a problem of Diophantus.Acta Arith. 65(1993), 15–27.zbMATHMathSciNetGoogle Scholar
  3. [3]
    —, On Diophantine quintuples.Acta Arith. 81 (1997), 69–79.zbMATHMathSciNetGoogle Scholar
  4. [4]
    G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern.Invent. Math. 73(1983), 349–366.CrossRefMathSciNetGoogle Scholar
  5. [5]
    W. Fulton,Algebraic Curves, An Introduction to Algebraic Geometry. W.A. Benjamin, Inc. 1969.Google Scholar
  6. [6]
    J. Gebel andH. G. Zimmer, Computing the Mordell-Weil group of an elliptic curve over ℚ. In: Elliptic Curves and Related Topics. Eds. H. Kisilevsky and M. Ram Murty.CRM Proc. and Lect. Notes, Amer. Math. Soc, Providence, R.I., 1994, 61–83.Google Scholar
  7. [7]
    S. Lang,Elliptic Curves: Diophantine Analysis. Springer, 1978.Google Scholar
  8. [8]
    K. Mahler, Über die rationalen Punkte auf Kurven vom Geschlecht Eins.J. reine angew. Math. 170 (1934), 168–178.zbMATHGoogle Scholar
  9. [9]
    A. Pethő,H. G. Zimmer,J. Gebel, andE. Herrmann, Computing all S-integral points on elliptic curves.J. Cambridge Math. Soc., to appear.Google Scholar
  10. [10]
    A. Pethő,E. Herrmann, andH. G. Zimmer, S-integral points on elliptic curves and Fermat’s triple equations. In: Algorithmic Number Theory, Ed.: J.P. Buhler,LNCS 1423, Springer, 1998, pp 528–540.Google Scholar
  11. [11]
    J. H. Silverman,The Arithmetic of Elliptic Curves. Graduate Texts in Math.,106, Springer, 1986.Google Scholar
  12. [12]
    SIMATH manual, Saarbrücken 1997.Google Scholar
  13. [13]
    B. M. M. DE Weger,Algorithms for diophantine equations. PhD Thesis, Centr. f. Wiskunde en Informatica, Amsterdam 1987.Google Scholar
  14. [14]
    D. Zagier, Large integral points on elliptic curves.Math. Comp. 48 (1987), 425–436.zbMATHCrossRefMathSciNetGoogle Scholar
  15. [15]
    —, Elliptische Kurven: Fortschritte und Anwendungen,Jber. d. Dtsch. Math.- Verein. 92(1990), 58–76.zbMATHMathSciNetGoogle Scholar

Copyright information

© Mathematische Seminar 1999

Authors and Affiliations

  1. 1.Fachbereich 9 MathematikUniversität des SaarlandesSaarbrückenGermany
  2. 2.Institut of Mathematics and InformaticsKossuth Lajos UniversityDebrecenHungary

Personalised recommendations