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On the diophantine equation

Authors:	Yann Bugeaud

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

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 $x^{2} - 2^{m} = \pm \, y^{n}$ , , , , $n \in \mathbf {N}$ , gcd, , has only finitely many solutions, all of which satisfying $n \le 7.3 \, 10^{5}$ .

Keywords:	Exponential equations linear forms in logarithms

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