On the diophantine equation x 2 - p m = ± y n

Yann Bugeaud

Acta Arithmetica (1997)

  • Volume: 80, Issue: 3, page 213-223
  • ISSN: 0065-1036

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Yann Bugeaud. "On the diophantine equation $x^2 - p^m = ±y^n$." Acta Arithmetica 80.3 (1997): 213-223. <http://eudml.org/doc/207038>.

@article{YannBugeaud1997,
author = {Yann Bugeaud},
journal = {Acta Arithmetica},
keywords = {exponential diophantine equation; Baker's method; linear forms in two logarithms},
language = {eng},
number = {3},
pages = {213-223},
title = {On the diophantine equation $x^2 - p^m = ±y^n$},
url = {http://eudml.org/doc/207038},
volume = {80},
year = {1997},
}

TY - JOUR
AU - Yann Bugeaud
TI - On the diophantine equation $x^2 - p^m = ±y^n$
JO - Acta Arithmetica
PY - 1997
VL - 80
IS - 3
SP - 213
EP - 223
LA - eng
KW - exponential diophantine equation; Baker's method; linear forms in two logarithms
UR - http://eudml.org/doc/207038
ER -

References

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  1. [1] Y. Bugeaud, On the diophantine equation x 2 - 2 m = ± y n , Proc. Amer. Math. Soc., to appear. Zbl0893.11012
  2. [2] Y. Bugeaud et M. Laurent, Minoration effective de la distance p-adique entre puissances de nombres algébriques, J. Number Theory 61 (1996), 311-342 
  3. [3] A. Faisant, L'équation diophantienne du second degré, Hermann, Paris, 1991. 
  4. [4] Y. D. Guo and M. H. Le, A note on the exponential diophantine equation x 2 - 2 m = y n , Proc. Amer. Math. Soc. 123 (1995), 3627-3629. 
  5. [5] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Clarendon Press, Oxford, 1990. Zbl0020.29201
  6. [6] C. Ko, On the diophantine equation x 2 = y n + 1 , xy ≠ 0, Sci. Sinica 14 (1965), 457-460. Zbl0163.04004
  7. [7] S. V. Kotov, Über die maximale Norm der Idealteiler des Polynoms a x m + b y n mit den algebraischen Koeffizienten, Acta Arith. 31 (1976), 219-230. Zbl0352.12002
  8. [8] 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
  9. [9] M. H. Le, On the generalized Ramanujan-Nagell equation, III, Dongbei Shuxue 4 (1988), 180-184. Zbl0669.10033
  10. [10] M. H. Le, The diophantine equation x 2 + D m = p n , Acta Arith. 52 (1989), 255-265. 
  11. [11] M. H. Le, Applications of Baker's method, IV, J. Changsha Railway Inst. 9 (1991), no. 2, 87-92. Zbl0891.11019
  12. [12] M. H. Le, A note on the diophantine equation ( x m - 1 ) / ( x - 1 ) = y n , Acta Arith. 64 (1993), 19-28. 
  13. [13] M. H. Le, Upper bounds for class number of real quadratic fields, ibid. 68 (1994), 141-144. Zbl0816.11055
  14. [14] M. H. Le, Some exponential diophantine equations, I, J. Number Theory 55 (1995), 209-221. Zbl0852.11015
  15. [15] T. N. Shorey, A. J. Van der Poorten, R. Tijdeman and A. Schinzel, Applications of the Gel'fond-Baker method to diophantine equations, in: Transcendence Theory: Advances and Applications, Academic Press, London, 1977, 59-78. Zbl0371.10015
  16. [16] M. Toyoizumi, On the diophantine equation x 2 + D m = p n , Acta Arith. 42 (1983), 303-309. Zbl0554.10008

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