On the Lebesgue–Nagell equation
Volume 125 / 2011
Colloquium Mathematicum 125 (2011), 245-253
MSC: 11D61, 11Y50, 11D41.
DOI: 10.4064/cm125-2-9
Abstract
We completely solve the Diophantine equations $x^2+2^aq^b=y^n$ (for $q=17, 29, 41$). We also determine all $C=p_1^{a_1}\cdots p_k^{a_k}$ and $C=2^{a_0}p_1^{a_1}\cdots p_k^{a_k}$, where $p_1,\ldots,p_k$ are fixed primes satisfying certain conditions. The corresponding Diophantine equations $x^2+C=y^n$ may be studied by the method used by Abu Muriefah et al. (2008) and Luca and Togbé (2009).
