Proceedings of the American Mathematical Society

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



A note on the exponential Diophantine equation $ x\sp 2-2\sp m=y\sp n$

Authors: Yongdong Guo and Mao Hua Le
Journal: Proc. Amer. Math. Soc. 123 (1995), 3627-3629
MSC: Primary 11D61
MathSciNet review: 1291786
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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.

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Article copyright: © Copyright 1995 American Mathematical Society