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Thue equations with composite fields

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  • Forschungsinstitut für Mathematik, ETH-Zentrum, CH-8092 Zürich, Switzerland
  • Algorithmique Arithmétique Expérimentale (A2X), UMR CNRS 9936, Université Bordeaux 1, 351, cours de la Libération, F-33405 Talence Cedex, France
Bibliografia
  • [1] A. Baker and H. Davenport, The equations 3x² - 2 = y² and 8x² - 7 = z², Quart. J. Math. Oxford Ser. (2) 20 (1969), 129-137.
  • [2] A. Baker and G. Wüstholz, Logarithmic forms and group varieties, J. Reine Angew. Math. 442 (1993), 19-62.
  • [3] Yu. Bilu, Solving superelliptic Diophantine equations by the method of Gelfond-Baker, preprint 94-09, Mathématiques Stochastiques, Univ. Bordeaux 2, 1994.
  • [4] Yu. Bilu and G. Hanrot, Solving Thue equations of high degree, J. Number Theory 60 (1996), 373-392.
  • [5] Yu. Bilu and G. Hanrot, Solving superelliptic Diophantine equations by Baker's method, Compositio Math. 112 (1998), 273-312.
  • [6] Yu. Bilu, G. Hanrot and P. M. Voutier, Existence of primitive divisors of Lucas and Lehmer numbers, submitted.
  • [7] Z. I. Borevich and I. R. Shafarevich, Number Theory, Academic Press, New York, 1966.
  • [8] H. Cohen, A Course in Computational Algebraic Number Theory, Grad. Texts in Math. 138, Springer, 1993.
  • [9] G. Hanrot, Résolution effective d'équations diophantiennes: algorithmes et applications, Thèse, Université Bordeaux 1, 1997.
  • [10] G. Hanrot, Solving Thue equations without the full unit group, Math. Comp., to appear.
  • [11] A. K. Lenstra, H. W. Lenstra, jr., and L. Lovász, Factoring polynomials with rational coefficients, Math. Ann. 261 (1982), 515-534.
  • [12] A. Pethő, Computational methods for the resolution of Diophantine equations, in: R. A. Mollin (ed.), Number Theory: Proc. First Conf. Canad. Number Theory Assoc. (Banff, 1988), de Gruyter, 1990, 477-492.
  • [13] A. Pethő and B. M. M. de Weger, Products of prime powers in binary recurrence sequences, Part I: The hyperbolic case, with an application to the generalized Ramanujan-Nagell equation, Math. Comp. 47 (1987), 713-727.
  • [14] M. E. Pohst, Computational Algebraic Number Theory, DMV Sem. 21, Birkhäuser, Basel, 1993.
  • [15] M. E. Pohst and H. Zassenhaus, Algorithmic Algebraic Number Theory, Cambridge Univ. Press, 1989.
  • [16] N. Smart, The solution of triangularly connected decomposable form equations, Math. Comp. 64 (1995), 819-840.
  • [17] C. Stewart, Primitive divisors of Lucas and Lehmer numbers, in: Transcendence Theory: Advances and Applications, A. Baker and D. W. Masser (eds.), Academic Press, 1977.
  • [18] N. Tzanakis and B. M. M. de Weger, On the practical solution of the Thue equation, J. Number Theory 31 (1989), 99-132.
  • [19] N. Tzanakis and B. M. M. de Weger, How to explicitly solve a Thue-Mahler equation, Compositio Math. 84 (1992), 223-288.
  • [20] P. Voutier, Primitive divisors of Lucas and Lehmer sequences, Math. Comp. 64 (1995), 869-888.
  • [21] B. M. M. de Weger, Solving exponential diophantine equations using lattice basis reduction algorithms, J. Number Theory 26 (1987), 325-367.
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Bibliografia
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