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Transactions of the American Mathematical Society

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On the generalized Ramanujan-Nagell equation $ x\sp 2-D=2\sp {n+2}$


Author: Mao Hua Le
Journal: Trans. Amer. Math. Soc. 334 (1992), 809-825
MSC: Primary 11D61
DOI: https://doi.org/10.1090/S0002-9947-1992-1070350-7
MathSciNet review: 1070350
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Abstract: Let $ D$ be a positive integer which is odd. In this paper we prove that the equation $ {x^2} - D = {2^{n + 2}}$ has at most three positive integer solutions $ (x,n)$ except when $ D = {2^{2m}} - 3 \cdot {2^{m + 1}} + 1$ , where $ m$ is a positive integer with $ m \geq 3$ .


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DOI: https://doi.org/10.1090/S0002-9947-1992-1070350-7
Article copyright: © Copyright 1992 American Mathematical Society