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arXiv · 1811.10118

An application of the modular method and the symplectic argument to a Lebesgue-Nagell equation

Angelos Koutsianas
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Abstract

In this paper, we study the generalized Lebesgue-Nagell equation \[ x^2+7^{2k+1}=y^n. \] This is the last case of equations of the form $x^2+q^{2k+1}=y^n$ with $k\geq0$ and $q>0$ where $\mathbb{Q}(\sqrt{-q})$ has class number one. Our proof is based on the modular method and the symplectic argument.

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Angelos Koutsianas. 2018-11-25. An application of the modular method and the symplectic argument to a Lebesgue-Nagell equation. https://arxiv.org/abs/1811.10118

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