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Experimental Mathematics Volume 4, 1995 - Issue 4
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Original Articles

Catalan's Equation Has No New Solution with Either Exponent Less Than 10651

Maurice Mignotte Universite Louis Pasteur, Centre de Calcul de l'Esplanade, 7, rue René Descartes, F-67084, Strasbourg, France E-mail: [email protected]
&
Yves Roy Universite Louis Pasteur, Centre de Calcul de l'Esplanade, 7, ru e Rene Descartes, F-67084, Strasbourg, France E-mail: [email protected]
Pages 259-268 | Published online: 03 Apr 2012

REFERENCES

  • Cassels , J. W. S. 1960 . “On the equation ax– by= 1, II” . Proc. Cambridge Society , 56 : 97 – 103 . [Cassels 1960]
  • Hyyrö , S. 1964 . “Über das Catalansche Problem” . Ann. Univ. Turku , 79 : 10 [Hyyrö 1964], Ser. AI
  • Inkeri , K. 1964 . “On Catalan's problem” . Acta Arith. , 9 : 285 – 290 . [Inkeri 1964]
  • Inkeri , K. 1990 . “On Catalan's conjecture” . J. Number Theory , 34 : 142 – 152 . [Inkeri 1990]
  • Chao , Ko . 1965 . “On the diophantine equation x2= yn+ l, xy ≠ 0” . Sci. Sinica , 14 : 457 – 460 . [Ko 1965]
  • Langevin , M. 1977/78 . “Quelques applications de nouveaux résultats de van der Poorten”. ” . In Sém. Delange-Pisot-Poitou 7 Paris [Langevin 1977], Exp. 4
  • Laurent , M. , Mignotte , M. and Nesterenko , Y. “Formes linéaires en deux logarithmes et déterminants d'interpolation” [Laurent et al.], to appear in J. Number Theory.
  • Mignotte , M. 1992 . “Sur l'équation de Catalan” . C. R. Acad. Sci. Paris, Sér. I , 314 : 165 – 168 . [Mignotte 1992]
  • Mignotte , M. 1993 . “Un critére élémentaire pour l'équation de Catalan” . C. R. Math. Rep. Acad. Sci. Canada , 15 : 199 – 200 . [Mignotte 1993]
  • Mignotte , M. 1994 . “Sur l'équation de Catalan (II)” . Theoret. Comp. Sci. , 123 : 145 – 149 . [Mignotte 1994]
  • Mignotte , M. 1995 . “A criterion on Catalan's equation” . J. Number Theory , 52 : 280 – 283 . [Mignotte 1995]
  • 1920 . “Des équations indéterminées x2+ x+1 = ynet x2+ x + l = 3yn“ . Nordsk. Mat. Forenings, Skr. (1) , 2 : 14 [Nagell 1920]
  • Ribenboim , P. 1994 . Catalan's conjecture Boston : Academic Press. . [Ribenboim 1994]
  • Tijdeman , R. 1976 . “On the equation of Catalan” . Acta Arith. , 29 : 197 – 209 . [Tijdeman 1976]
  • Schwarz , W. 1995 . “A note on Catalan's equation” . Acta Arith. , 72 : 277 – 279 . [Schwarz 1995]
  • Washington , L. C. 1982 . Introduction to cyclotomic fields New York : Springer. . [Washington 1982]

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