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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the diophantine equation $x^2-2^m=\pm y^n$
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by Yann Bugeaud PDF
Proc. Amer. Math. Soc. 125 (1997), 3203-3208 Request permission

Abstract:

One of the purposes of this note is to correct the proof of a recent result of Y. Guo & M. Le on the equation $x^{2} - 2^{m} = y^{n}$. Moreover, we prove that the diophantine equation $x^{2} - 2^{m} = \pm y^{n}$, $x$, $y$, $m$, $n \in \mathbf {N}$, gcd$(x, y) =1$, $y>1$, $n>2$ has only finitely many solutions, all of which satisfying $n \le 7.3 10^{5}$.
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Additional Information
  • Yann Bugeaud
  • Affiliation: Université Louis Pasteur, U. F. R. de mathématiques, 7, rue René Descartes, 67084 Strasbourg, France
  • Address at time of publication: 31 rue de l’Etang, 56600 Lanester, France
  • Email: bugeaud@pari.u-strasbg.fr
  • Received by editor(s): June 13, 1996
  • Communicated by: William W. Adams
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 3203-3208
  • MSC (1991): Primary 11D61, 11J86
  • DOI: https://doi.org/10.1090/S0002-9939-97-04093-8
  • MathSciNet review: 1422850