On the Lebesgue–Nagell equation

Volume 125 / 2011

Andrzej Dąbrowski Colloquium Mathematicum 125 (2011), 245-253 MSC: 11D61, 11Y50, 11D41. DOI: 10.4064/cm125-2-9


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).


  • Andrzej DąbrowskiInstitute of Mathematics
    University of Szczecin
    Wielkopolska 15
    70-451 Szczecin, Poland

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