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Complete solution of a family of quartic Thue equations

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References

  1. A. Baker. Contribution to the theory of Diophantine equations I. On the representation of integers by binary forms.Philos. Trans. Roy. Soc. Londen 263 (1968), 173–191.

    Article  MATH  Google Scholar 

  2. I. Gaál. On the resolution of some diophantine equations. In:Computational Number Theory, Colloquim on Computational Number Theory, Debrecen, 1989. Eds.: A. Pethő, M. Pohst, H.C. Williams, H.G. Zimmer. De Gruyter 1991, 261–280.

  3. I. Gaál, A. Pethő andM. Pohst. On the resolution of a family of index form equations in quartic number fields.J. Symbolic Comp. 16 (1993), 563–584.

    Article  MATH  Google Scholar 

  4. I. Gaál, A. Pethő andM. Pohst. Simultaneous representation of integers by a pair of ternary quadratic forms with an application to index form equations in quartic number fields.J. Number Theory, to appear.

  5. M. N. Gras. Table numerique du nombre de classe et des unites des extensions cycliques reelles de degré 4 de ℒ.Publ. Math. Fac. Sci. Besançon (1977–1978), fasc. 2.

  6. A. J. Lazarus. On the class number and unit index of simplest quartic fields.Nagoya Math. J. 121 (1991), 1–13.

    MATH  MathSciNet  Google Scholar 

  7. K. Mahler. An inequality for the discriminant of a polynomial.Michigan Math. J. 11 (1964), 257–262.

    Article  MATH  MathSciNet  Google Scholar 

  8. M. Mignotte. Verification of a Conjecture of E. Thomas.J. Number Theory 44 (1993), 172–177.

    Article  MATH  MathSciNet  Google Scholar 

  9. M. Mignotte, A. Pethő andR. Roth. Complete solutions of quartic Thue and index form equations.Math. Comp., to appear.

  10. M. Mignotte andN. Tzanakis. On a family of cubics.J. Number Theory 39 (1991), 41–49.

    Article  MATH  MathSciNet  Google Scholar 

  11. A. Pethő. Complete solutions to families of quartic Thue equations.Math. Comp. 57 (1991), 777–798.

    Article  MathSciNet  Google Scholar 

  12. A. Pethő andR. Schulenberg. Effektives Lösen von Thue Gleichungen.Publ. Math. Debrecen 34 (1987), 189–196.

    MathSciNet  Google Scholar 

  13. M. Pohst andH. Zassenhaus.Algorithmic Algebraic Number Theory. Cambridge Univ. Press 1989.

  14. D. Shanks. The simplest cubic fields.Math. Comp. 28 (1974), 1134–1152.

    Google Scholar 

  15. E. Thomas. Fundamental units for orders in certain cubic number fields.J. reine angew. Math. 310 (1979), 33–55.

    MATH  MathSciNet  Google Scholar 

  16. E. Thomas. Complete solutions to a family of cubic diophantine equations.J. Number Theory 34 (1990), 235–250.

    Article  MATH  MathSciNet  Google Scholar 

  17. E. Thomas. Solutions to certain families of Thue equations.J. Number Theory 43 (1993), 319–369.

    Article  MATH  MathSciNet  Google Scholar 

  18. A. Thue. Über Annäherungswerte algebraischer Zahlen.J. reine angew. Math. 135 (1909), 284–305.

    MATH  Google Scholar 

  19. N. Tzanakis andB. M. M. de Weger. On the practical solution of the Thue equation.J. Number Theory 31 (1989), 99–132.

    Article  MATH  MathSciNet  Google Scholar 

  20. M. Waldschmidt.Linear independence of logarithms of algebraic numbers. IMSc. Report116, The Institute of Math. Sciences. Madras 1992.

    MATH  Google Scholar 

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Author notes

  1. G. Lettl

    Present address: Institut für Mathematik, Karl-Franzens-Universität, Heinrichstraße 36, 8010, Graz, Australia

  2. A. Pethő

    Present address: Laboratory of Informatics, University of Medicine, Nagyerdei krt. 98, 4032, Debrecen, Hungary

Authors and Affiliations

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    1. G. Lettl
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    2. A. Pethő
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    Additional information

    This paper evolved from a visit of the first author to the University of Debrecen, Hungary, which was supported by the Austrian-Hungarian Science Cooperation project Nr. 10-U-3. Research of the second author was partially supported by Hungarian National Foundation for Scientific Research Grant 1641/90.

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    Lettl, G., Pethő, A. Complete solution of a family of quartic Thue equations. Abh.Math.Semin.Univ.Hambg. 65, 365–383 (1995). https://doi.org/10.1007/BF02953340

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