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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On the generalized Ramanujan-Nagell equation $x^ 2-D=2^ {n+2}$
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by Mao Hua Le PDF
Trans. Amer. Math. Soc. 334 (1992), 809-825 Request permission

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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Additional Information
  • © Copyright 1992 American Mathematical Society
  • 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