A note on the equation a x n - b y n = c

Maurice Mignotte

Acta Arithmetica (1996)

  • Volume: 75, Issue: 3, page 287-295
  • ISSN: 0065-1036

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Maurice Mignotte. "A note on the equation $ax^n - by^n = c$." Acta Arithmetica 75.3 (1996): 287-295. <http://eudml.org/doc/206878>.

@article{MauriceMignotte1996,
author = {Maurice Mignotte},
journal = {Acta Arithmetica},
keywords = {exponential diophantine equations; absolute upper bound for the degree ; explicit lower bound; binary form of degree ; linear forms in two logarithms of algebraic numbers},
language = {eng},
number = {3},
pages = {287-295},
title = {A note on the equation $ax^n - by^n = c$},
url = {http://eudml.org/doc/206878},
volume = {75},
year = {1996},
}

TY - JOUR
AU - Maurice Mignotte
TI - A note on the equation $ax^n - by^n = c$
JO - Acta Arithmetica
PY - 1996
VL - 75
IS - 3
SP - 287
EP - 295
LA - eng
KW - exponential diophantine equations; absolute upper bound for the degree ; explicit lower bound; binary form of degree ; linear forms in two logarithms of algebraic numbers
UR - http://eudml.org/doc/206878
ER -

References

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  1. [B] A. Baker, On the representation of integers by binary forms, Philos. Trans. Roy. Soc. London Ser. A 263 (1968), 173-191. Zbl0157.09702
  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 a x r - b y r = 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. Zbl0349.10028
  6. [ST] T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge University Press, 1986. Zbl0606.10011
  7. [Th] A. Thue, Berechnung aller Lösungen gewisser Gleichungen der Form a x r - b y r = 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 

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