On the Lebesgue-Nagell equation
Colloquium Mathematicae (2011)
- Volume: 125, Issue: 2, page 245-253
- ISSN: 0010-1354
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topAndrzej Dąbrowski. "On the Lebesgue-Nagell equation." Colloquium Mathematicae 125.2 (2011): 245-253. <http://eudml.org/doc/283944>.
@article{AndrzejDąbrowski2011,
abstract = {We completely solve the Diophantine equations $x² + 2^\{a\}\{q\}^b = yⁿ$ (for q = 17, 29, 41). We also determine all $C = p₁^\{a₁\} ⋯ p_k^\{a_k\}$ and $C = 2^\{a₀\}p₁^\{a₁\} ⋯ p_k^\{a_k\}$, where $p₁,...,p_k$ 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).},
author = {Andrzej Dąbrowski},
journal = {Colloquium Mathematicae},
keywords = {Diophantine equations; exponential equations; elliptic curves},
language = {eng},
number = {2},
pages = {245-253},
title = {On the Lebesgue-Nagell equation},
url = {http://eudml.org/doc/283944},
volume = {125},
year = {2011},
}
TY - JOUR
AU - Andrzej Dąbrowski
TI - On the Lebesgue-Nagell equation
JO - Colloquium Mathematicae
PY - 2011
VL - 125
IS - 2
SP - 245
EP - 253
AB - We completely solve the Diophantine equations $x² + 2^{a}{q}^b = yⁿ$ (for q = 17, 29, 41). We also determine all $C = p₁^{a₁} ⋯ p_k^{a_k}$ and $C = 2^{a₀}p₁^{a₁} ⋯ p_k^{a_k}$, where $p₁,...,p_k$ 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).
LA - eng
KW - Diophantine equations; exponential equations; elliptic curves
UR - http://eudml.org/doc/283944
ER -
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