ArticleOriginal scientific text

Title

A note on the equation axn-byn=c

Authors 1

Affiliations

  1. Institut de Mathématiques, Université Louis Pasteur, 7, rue René Descartes, 67084 Strasbourg, France

Bibliography

  1. [B] A. Baker, On the representation of integers by binary forms, Philos. Trans. Roy. Soc. London Ser. A 263 (1968), 173-191.
  2. [LMN] M. Laurent, M. Mignotte et Y. Nesterenko, Formes linéaires en deux logarithmes et déterminants d'interpolation, J. Number Theory 55 (1995), 285-321.
  3. [M] L. J. Mordell, Diophantine Equations, Academic Press, London, 1969.
  4. [S] C. L. Siegel, Die Gleichung axr-byr=c, Math. Ann. 144 (1937), 57-68. Also Gesammelte Abhandlungen, II (1966).
  5. [Sh] T. N. Shorey, Linear forms in the logarithms of algebraic numbers with small coefficients I, J. Indian Math. Soc. 38 (1974), 271-284.
  6. [ST] T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge University Press, 1986.
  7. [Th] A. Thue, Berechnung aller Lösungen gewisser Gleichungen der Form axr-byr=f, Vid. Selskap Skrifter Kristiana Mat. Natur. Kl. (1918), No 4.
  8. [Ti] R. Tijdeman, Some applications of Baker's sharpened bounds to diophantine equations, Séminaire Delange-Pisot-Poitou, 1974/75, Exp. 27, Paris, 7 pp.
  9. [W] M. Waldschmidt, Minorations de combinaisons linéaires de logarithmes de nombres algébriques, Canad. J. Math. 45 (1993), 176-224
Pages:
287-295
Main language of publication
English
Received
1995-07-16
Accepted
1995-11-17
Published
1996
Exact and natural sciences