Thue equations with composite fields

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1. [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. [2] A. Baker and G. Wüstholz, Logarithmic forms and group varieties, J. Reine Angew. Math. 442 (1993), 19-62. Zbl0788.11026
3. [3] Yu. Bilu, Solving superelliptic Diophantine equations by the method of Gelfond-Baker, preprint 94-09, Mathématiques Stochastiques, Univ. Bordeaux 2, 1994. 
4. [4] Yu. Bilu and G. Hanrot, Solving Thue equations of high degree, J. Number Theory 60 (1996), 373-392. Zbl0867.11017
5. [5] Yu. Bilu and G. Hanrot, Solving superelliptic Diophantine equations by Baker's method, Compositio Math. 112 (1998), 273-312. Zbl0915.11065
6. [6] Yu. Bilu, G. Hanrot and P. M. Voutier, Existence of primitive divisors of Lucas and Lehmer numbers, submitted. Zbl0995.11010
7. [7] Z. I. Borevich and I. R. Shafarevich, Number Theory, Academic Press, New York, 1966. 
8. [8] H. Cohen, A Course in Computational Algebraic Number Theory, Grad. Texts in Math. 138, Springer, 1993. 
9. [9] G. Hanrot, Résolution effective d'équations diophantiennes: algorithmes et applications, Thèse, Université Bordeaux 1, 1997. 
10. [10] G. Hanrot, Solving Thue equations without the full unit group, Math. Comp., to appear. Zbl0937.11063
11. [11] A. K. Lenstra, H. W. Lenstra, jr., and L. Lovász, Factoring polynomials with rational coefficients, Math. Ann. 261 (1982), 515-534. Zbl0488.12001
12. [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. Zbl0704.11006
13. [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. Zbl0623.10011
14. [14] M. E. Pohst, Computational Algebraic Number Theory, DMV Sem. 21, Birkhäuser, Basel, 1993. 
15. [15] M. E. Pohst and H. Zassenhaus, Algorithmic Algebraic Number Theory, Cambridge Univ. Press, 1989. Zbl0685.12001
16. [16] N. Smart, The solution of triangularly connected decomposable form equations, Math. Comp. 64 (1995), 819-840. Zbl0831.11027
17. [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. Zbl0366.12002
18. [18] N. Tzanakis and B. M. M. de Weger, On the practical solution of the Thue equation, J. Number Theory 31 (1989), 99-132. Zbl0657.10014
19. [19] N. Tzanakis and B. M. M. de Weger, How to explicitly solve a Thue-Mahler equation, Compositio Math. 84 (1992), 223-288. Zbl0773.11023
20. [20] P. Voutier, Primitive divisors of Lucas and Lehmer sequences, Math. Comp. 64 (1995), 869-888. Zbl0832.11009
21. [21] B. M. M. de Weger, Solving exponential diophantine equations using lattice basis reduction algorithms, J. Number Theory 26 (1987), 325-367. Zbl0625.10013