On the diophantine equation D₁x⁴ -D₂y² = 1

Maohua Le

Acta Arithmetica (1996)

  • Volume: 76, Issue: 1, page 1-9
  • ISSN: 0065-1036

How to cite

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Maohua Le. "On the diophantine equation D₁x⁴ -D₂y² = 1." Acta Arithmetica 76.1 (1996): 1-9. <http://eudml.org/doc/206886>.

@article{MaohuaLe1996,
author = {Maohua Le},
journal = {Acta Arithmetica},
keywords = {exponential diophantine equation; upper bound for solutions; Baker's method},
language = {eng},
number = {1},
pages = {1-9},
title = {On the diophantine equation D₁x⁴ -D₂y² = 1},
url = {http://eudml.org/doc/206886},
volume = {76},
year = {1996},
}

TY - JOUR
AU - Maohua Le
TI - On the diophantine equation D₁x⁴ -D₂y² = 1
JO - Acta Arithmetica
PY - 1996
VL - 76
IS - 1
SP - 1
EP - 9
LA - eng
KW - exponential diophantine equation; upper bound for solutions; Baker's method
UR - http://eudml.org/doc/206886
ER -

References

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  1. [1] M. Laurent, M. Mignotte et Y. Nesterenko, Formes linéaires en deux logarithmes et déterminants d'interpolation, J. Number Theory 55 (1995), 285-321. Zbl0843.11036
  2. [2] M.-H. Le, A necessary and sufficient condition for the equation x⁴ - Dy² = 1 to having positive integer solutions, Chinese Sci. Bull. 30 (1985), 1698. 
  3. [3] M.-H. Le, A note on the diophantine equation x 2 p - D y ² = 1 , Proc. Amer. Math. Soc. 107 (1989), 27-34. 
  4. [4] W. Ljunggren, Über die Gleichung x⁴ - Dy² = 1, Arch. Math. Naturv. 45 (5) (1942), 61-70. Zbl68.0069.01
  5. [5] K. Petr, Sur l'équation de Pell, Časopis Pest. Mat. Fys. 56 (1927), 57-66 (in Czech). 
  6. [6] H.-M. Wu, On the number of solutions of the diophantine equation x⁴ - Dy² = 1, J. Zhanjiang Teachers College Nat. Sci. 1995 (1), 12-15 (in Chinese). 
  7. [7] W.-S. Zhu, The solvability of equation x⁴ - Dy² = 1, Acta Math. Sinica 28 (1985), 681-683 (in Chinese). Zbl0587.10009

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