欧拉与五边形数定理
Euler and the pentagonal number theorem
摘要：
``在本文中，我们给历史的莱昂哈德欧拉的工作对五边形数定理，和他的应用五边形数定理的除数函数，分拆函数和发散级数。我们试图给一个详尽的审查所有欧拉的信件和出版物的五边形数定理和他的应用。本文详尽地总结了欧拉关于五边形数定理的工作。我已经通过了所有欧拉的出版信件（除了杜莫佩屠斯和弗雷德里克二世）和他的论文，以找到每次他讨论的五边形数定理或应用。我已经翻译了拉丁美洲的许多部分，他的信件和论文，是不是在英语，也部分在法国和德国与博士保罗Mezo和基督教Leger。
英文摘要：
``In this paper we give the history of Leonhard Euler's work on the pentagonal number theorem, and his applications of the pentagonal number theorem to the divisor function, partition function and divergent series. We have attempted to give an exhaustive review of all of Euler's correspondence and publications about the pentagonal number theorem and his applications of it.'' This paper gives an exhaustive summary of Euler's work on the pentagonal number theorem. I have gone through all of Euler's published correspondence (except with du Maupertuis and Frederic II) and his papers to find each time he discusses the pentagonal number theorem or applications of it. I have translated from the Latin many sections of his correspondence and papers that are not available in the English, and also sections in the French and German with Dr. Paul Mezo and Christian Leger.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
