Geodesic
On the Lebesgue–Nagell equation
Andrzej Dąbrowski1
1 Institute of Mathematics University of Szczecin Wielkopolska 15 70-451 Szczecin, Poland
Colloquium Mathematicum, Tome 125 (2011) no. 2, pp. 245-253

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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).
DOI : 10.4064/cm125-2-9
Mots-clés : completely solve diophantine equations determine cdots cdots where ldots fixed primes satisfying certain conditions corresponding diophantine equations may studied method abu muriefah luca togb

Andrzej Dąbrowski 1

1 Institute of Mathematics University of Szczecin Wielkopolska 15 70-451 Szczecin, Poland 
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Andrzej Dąbrowski. On the Lebesgue–Nagell equation. Colloquium Mathematicum, Tome 125 (2011) no. 2, pp. 245-253. doi: 10.4064/cm125-2-9

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