This article examines the research of Louis J. Mordell on the Diophantine equation $$y^2-k=x^3$$ as it appeared in one of his first papers, published in 1914. After presenting a number of elements relating to Mordell’s mathematical youth and his (problematic) writing, we analyze the 1914 paper by following the three approaches he developed therein, respectively, based on the quadratic reciprocity law, on ideal numbers, and on binary cubic forms. This analysis allows us to describe many of the difficulties in reading and understanding Mordell’s proofs, difficulties which we make explicit and comment on in depth.

中文翻译：

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路易斯 J.莫德尔关于丢番图方程 $$y^2-k=x^3$$ y 2 - k = x 3 的年轻著作

本文考察了 Louis J. Mordell 对丢番图方程 $$y^2-k=x^3$$ 的研究，该方程出现在他 1914 年发表的第一篇论文中。数学青年和他的（有问题的）写作，我们按照他在其中开发的三种方法来分析 1914 年的论文，分别基于二次互易律、理想数和二进制三次形式。这种分析使我们能够描述阅读和理解莫德尔证明的许多困难，我们对这些困难进行了明确和深入的评论。