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Zbl 1074.11022
Siksek, Samir
On the Diophantine equation $x^2= y^p+2^kz^p$. (English)
[J] J. Théor. Nombres Bordx. 15, No. 3, 839-846 (2003). ISSN 1246-7405

The equation of the title is attacked using a Frey curve, Ribet's level-lowering theorem and a method due to Darmon and Merel. All the solutions in pairwise coprime integers $x, y, z$ $(p \geq 7, k \geq 2)$ are determined. In particular, previous results of various authors are combined to obtain a complete solution for the equation $x^2 + 2^k = y^n$ for $n \geq 3$.
[Edward L. Cohen (Ottawa)]

MSC 2000:: *11D61 Exponential diophantine equations

Keywords: exponential Diophantine equations; elliptic curves

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