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

M. Mignotte; A. Pethő; F. Lemmermeyer

Acta Arithmetica (1996)

  • Volume: 76, Issue: 3, page 245-269
  • ISSN: 0065-1036

How to cite


M. Mignotte, A. Pethő, and F. Lemmermeyer. "On the family of Thue equations x³ - (n-1)x²y - (n+2)xy² - y³ = k." Acta Arithmetica 76.3 (1996): 245-269. <http://eudml.org/doc/206898>.

author = {M. Mignotte, A. Pethő, F. Lemmermeyer},
journal = {Acta Arithmetica},
keywords = {cubic Thue equation; simplest cubic fields; bounds for the solutions; linear forms in logarithms; Liouville's inequality for rational approximations},
language = {eng},
number = {3},
pages = {245-269},
title = {On the family of Thue equations x³ - (n-1)x²y - (n+2)xy² - y³ = k},
url = {http://eudml.org/doc/206898},
volume = {76},
year = {1996},

AU - M. Mignotte
AU - A. Pethő
AU - F. Lemmermeyer
TI - On the family of Thue equations x³ - (n-1)x²y - (n+2)xy² - y³ = k
JO - Acta Arithmetica
PY - 1996
VL - 76
IS - 3
SP - 245
EP - 269
LA - eng
KW - cubic Thue equation; simplest cubic fields; bounds for the solutions; linear forms in logarithms; Liouville's inequality for rational approximations
UR - http://eudml.org/doc/206898
ER -


  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. Zbl0788.11026
  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. Zbl0851.11059
  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. Zbl0853.11021
  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. Zbl0853.11022
  10. [MT] M. Mignotte and N. Tzanakis, On a family of cubics, J. Number Theory 39 (1991), 41-49. Zbl0734.11025
  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. Zbl0738.11028
  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. Zbl0697.10011
  15. [T2] E. Thomas, Solutions to certain families of Thue equations, J. Number Theory 43 (1993), 319-369. Zbl0774.11013

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