Integral Points on Certain Elliptic Curves

Hui Lin Zhu; Jian Hua Chen

Rendiconti del Seminario Matematico della Università di Padova (2008)

  • Volume: 119, page 1-20
  • ISSN: 0041-8994

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Zhu, Hui Lin, and Chen, Jian Hua. "Integral Points on Certain Elliptic Curves." Rendiconti del Seminario Matematico della Università di Padova 119 (2008): 1-20. <http://eudml.org/doc/108734>.

@article{Zhu2008,
author = {Zhu, Hui Lin, Chen, Jian Hua},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {elliptic curves; integral points; number fields; unit group; class group},
language = {eng},
pages = {1-20},
publisher = {Seminario Matematico of the University of Padua},
title = {Integral Points on Certain Elliptic Curves},
url = {http://eudml.org/doc/108734},
volume = {119},
year = {2008},
}

TY - JOUR
AU - Zhu, Hui Lin
AU - Chen, Jian Hua
TI - Integral Points on Certain Elliptic Curves
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2008
PB - Seminario Matematico of the University of Padua
VL - 119
SP - 1
EP - 20
LA - eng
KW - elliptic curves; integral points; number fields; unit group; class group
UR - http://eudml.org/doc/108734
ER -

References

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  2. [2] R. J. STROEKER - N. TZANAKIS, Solving Elliptic Diophantine Equations by Estimating Linear Forms in Elliptic Logarithms, Acta Arith., 29(2) (1994), pp. 177-196. Zbl0805.11026MR1291875
  3. [3] R. J. STROEKER - N. TZANAKIS, On the Elliptic Logarithm Method for Elliptic Diophantine Equations: Reflections and an Improvement, Experimental Mathemetics, 8(2) (1999), pp. 135-149. Zbl0979.11060MR1700575
  4. [4] R. J. STROEKER - N. TZANAKIS, Computing All Integer Solutions of a Genus 1 Equation, Math. Comp., 72 (2003), pp. 1917-1933. Zbl1089.11019MR1986812
  5. [5] D. ZAGIER, Large Integral Point on Elliptic Curves, Math. Comp., 48(177) (1987), pp. 425-536. Zbl0611.10008MR866125
  6. [6] W. LJUNGGREN, A Diophantine Problem, Jour London Math. Soc., 3(2) (1971), pp. 385-391. Zbl0215.34701MR291077
  7. [7] J. H. CHEN, A Note on the Diophantine Equation x 2 + 1 = d y 4 , Abh. Math. Sem. Univ. Hamburg, 64 (1994), pp. 1-10. MR1292712
  8. [8] K. Q. FENG, Algebraic Number Theory, Science Press, 2000 (Chinese). 
  9. [9] L. G. HUA, Introduction to Number Theory, Science Press, 1979 (Chinese). Zbl0221.10002
  10. [10] R. J. STROEKER - N. TZANAKIS, On the Application of skolem's p-adic Method to the solution of Thue Equations, Journal of Number Theory, 29 (1988), pp. 166-195. Zbl0674.10012MR945593
  11. [11] W. LJUNGGREN, Solution complete de quelquls equations du sixieme, degre a deux indeterminees, Arch. Math., 48(7) (1946), pp. 26-29. Zbl0060.09103MR19647
  12. [12] N. TZANAKIS, On the Diophantine equation x2 – dy4 = k, Acta Arith., 46(3) (1986), pp. 257-269. Zbl0543.10017
  13. [13] L. J. MORDELL, Diophantine Equations, London: Academic Press, 1969. Zbl0188.34503MR249355
  14. [14] Z. F. CAO - S. Z. MU - X. L. DONG, A New Proof of a Conjecture of Antoniadis, Jour Number Theory, 83 (2000), pp. 185-193. Zbl0958.11025MR1772611
  15. [15] J. BUCHMANN, A generalization of Voronoi's unit algorithm (I II), Jour. Number Theory, 20 (1985), pp. 177-209. Zbl0575.12005MR790781
  16. [16] J. BUCHMANN, The Computation of the Fundamental Unit of Totally Comples Quartic Orders, Math. Comp., 48(177) (1987), pp. 39-54. Zbl0627.12004MR866097

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