Classical and modular approaches to exponential Diophantine equations II. The Lebesgue-Nagell equation

Yann Bugeaud; Maurice Mignotte; Samir Siksek

Classical and modular approaches to exponential Diophantine equations II. The Lebesgue-Nagell equation

Number Theory 2007-05-23 v1

Authors: Yann Bugeaud , Maurice Mignotte , Samir Siksek

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Abstract

We solve completely the Lebesgue-Nagell equation x^2+D=y^n, in integers x, y, n>2, for D in the range 1 =< D =< 100.

Keywords

exponential Diophantine equations Lebesgue-Nagell equation modular approach integer solutions number theory

Cite

@article{arxiv.math/0405220,
  title  = {Classical and modular approaches to exponential Diophantine equations II. The Lebesgue-Nagell equation},
  author = {Yann Bugeaud and Maurice Mignotte and Samir Siksek},
  journal= {arXiv preprint arXiv:math/0405220},
  year   = {2007}
}