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On the family of Thue equations x³ - (n-1)x²y - (n+2)xy² - y³ = k

Authors 1, 2, 3

Affiliations

  1. Département de Mathématique et Informatique, Université Louis Pasteur, 7, rue René Descartes, 67084 Strasbourg Cedex, France
  2. Laboratory of Informatics, University of Medicine, Nagyerdei Krt. 98, H-4032 Debrecen, Hungary
  3. Erwin-Rohde-Str. 19 D-69120 Heidelberg, Germany

Bibliography

  1. [BD] A. Baker and H. Davenport, The equations 3x²-2 = y² and 8x²-7 = z², Quart. J. Math. Oxford 20 (1969), 129-137.
  2. [BSt] A. Baker and C. L. Stewart, On effective approximations to cubic irrationals, in: New Advances in Transcendence Theory, Proc. Sympos., Durham 1986, A. Baker (ed.), Cambridge Univ. Press, 1988, 1-24.
  3. [BW] A. Baker and G. Wüstholz, Linear forms and group varieties, J. Reine Angew. Math. 442 (1993), 19-62.
  4. [GyP] K. Győry and Z. Z. Papp, Norm form equations and explicit lower bounds for linear forms with algebraic coefficients, in: Studies in Pure Mathematics (to the memory of Paul Turán), P. Erdős (ed.), Akadémiai Kiadó and Birkhäuser, Budapest, 1983, 245-257.
  5. [LMN] M. Laurent, M. Mignotte et Y. Nesterenko, Formes linéaires en deux logarithmes et déterminants d'interpolation, J. Number Theory 55 (1995), 285-321.
  6. [LP] F. Lemmermeyer and A. Pethő, Simplest number fields, Manuscripta Math. 88 (1995), 53-58.
  7. [LeP] G. Lettl and A. Pethő, Complete solution of a family of quartic Thue equations, Abh. Math. Sem. Univ. Hamburg 65 (1995), 365-383.
  8. [M] M. Mignotte, Verification of a conjecture of E. Thomas, J. Number Theory 44 (1993), 172-177.
  9. [MPR] M. Mignotte, A. Pethő and R. Roth, Complete solutions of quartic Thue and index form equations, Math. Comp. 65 (1996), 341-354.
  10. [MT] M. Mignotte and N. Tzanakis, On a family of cubics, J. Number Theory 39 (1991), 41-49.
  11. [P1] A. Pethő, On the representation of 1 by binary cubic forms with positive discriminant, in: Number Theory, Ulm 1987, H. P. Schlickewei and E. Wirsing (eds.), Lecture Notes in Math. 1380, Springer, 1989, 185-196.
  12. [P2] A. Pethő, Complete solutions to a family of quartic diophantine equations, Math. Comp. 57 (1991), 777-798.
  13. [PSch] A. Pethő und R. Schulenberg, Effektives Lösen von Thue Gleichungen, Publ. Math. Debrecen 34 (1987), 189-196.
  14. [T1] E. Thomas, Complete solutions to a family of cubic diophantine equations, J. Number Theory 34 (1990), 235-250.
  15. [T2] E. Thomas, Solutions to certain families of Thue equations, J. Number Theory 43 (1993), 319-369.
Acta Arithmetica
1996/76/3
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Pages:
245-269
Main language of publication
English
Received
1995-06-26
Accepted
1995-10-02
Published
1996
Exact and natural sciences