A note on the exponential Diophantine equation $x^ 2-2^ m=y^ n$
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- by Yongdong Guo and Mao Hua Le PDF
- Proc. Amer. Math. Soc. 123 (1995), 3627-3629 Request permission
Abstract:
In this note we prove that the equation ${x^2} - {2^m} = {y^n},x,y,m,n \in \mathbb {N},\gcd (x,y) = 1,y > 1,n > 2$, has only finitely many solutions (x, y, m, n). Moreover, all solutions of the equation satisfy $2\nmid mn,n < 2 \cdot {10^9}$ and $\max (x,y,m) < C$, where C is an effectively computable absolute constant.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 3627-3629
- MSC: Primary 11D61
- DOI: https://doi.org/10.1090/S0002-9939-1995-1291786-3
- MathSciNet review: 1291786