On the Lebesgue-Nagell equation

Andrzej Dąbrowski

Colloquium Mathematicae, Tome 122 (2011), p. 245-253 / Harvested from The Polish Digital Mathematics Library

Résumé

We completely solve the Diophantine equations $x ² + 2^{a} q^{b} = y ⁿ$ (for q = 17, 29, 41). We also determine all $C = p ₁^{a ₁} \dots p_{k}^{a_{k}}$ and $C = 2^{a ₀} p ₁^{a ₁} \dots p_{k}^{a_{k}}$ , where $p ₁, . . ., p_{k}$ are fixed primes satisfying certain conditions. The corresponding Diophantine equations x² + C = yⁿ may be studied by the method used by Abu Muriefah et al. (2008) and Luca and Togbé (2009).

Publié le : 2011-01-01

Zbl 1260.11020

EUDML-ID : urn:eudml:doc:283944

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     title = {On the Lebesgue-Nagell equation},
     journal = {Colloquium Mathematicae},
     volume = {122},
     year = {2011},
     pages = {245-253},
     zbl = {1260.11020},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm125-2-9}
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Andrzej Dąbrowski. On the Lebesgue-Nagell equation. Colloquium Mathematicae, Tome 122 (2011) pp. 245-253. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm125-2-9/