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

• Autorzy: Yann Bugeaud
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1997
• Tom: 80
• Numer: 3
• Strony: 213-223

Daty

wydano

1997

otrzymano

1996-05-28

poprawiono

1996-09-12

Twórcy

autor

Yann Bugeaud

• U.F.R. de mathématiques, Université Louis Pasteur, 7, rue René Descartes, 67084 Strasbourg, France

Bibliografia

• [1] Y. Bugeaud, On the diophantine equation $x^2 - 2^m = ±y^n$, Proc. Amer. Math. Soc., to appear.
• [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] A. Faisant, L'équation diophantienne du second degré, Hermann, Paris, 1991.
• [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] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Clarendon Press, Oxford, 1990.
• [6] C. Ko, On the diophantine equation $x^2 = y^n + 1$, xy ≠ 0, Sci. Sinica 14 (1965), 457-460.
• [7] S. V. Kotov, Über die maximale Norm der Idealteiler des Polynoms $ax^m + by^n$ mit den algebraischen Koeffizienten, Acta Arith. 31 (1976), 219-230.
• [8] M. Laurent, M. Mignotte et Y. Nesterenko, Formes linéaires en deux logarithmes et déterminants d'interpolation, J. Number Theory 55 (1995), 285-321.
• [9] M. H. Le, On the generalized Ramanujan-Nagell equation, III, Dongbei Shuxue 4 (1988), 180-184.
• [10] M. H. Le, The diophantine equation $x^2 + D^m = p^n$, Acta Arith. 52 (1989), 255-265.
• [11] M. H. Le, Applications of Baker's method, IV, J. Changsha Railway Inst. 9 (1991), no. 2, 87-92.
• [12] M. H. Le, A note on the diophantine equation $(x^m -1)/(x-1) = y^n$, Acta Arith. 64 (1993), 19-28.
• [13] M. H. Le, Upper bounds for class number of real quadratic fields, ibid. 68 (1994), 141-144.
• [14] M. H. Le, Some exponential diophantine equations, I, J. Number Theory 55 (1995), 209-221.
• [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.
• [16] M. Toyoizumi, On the diophantine equation $x^2 + D^m = p^n$, Acta Arith. 42 (1983), 303-309.