关于阿基米德牛群问题及与之有关的Pell方程

On Archimedes Cattle Problem and Associated Pell Equation

公元前251年阿基米德提出的太阳神牛群问题,至今仍是数学研究的一个热点问题,关于该问题的研究促进了初等数论和代数数论的发展,得到了许多有意义的结果。鉴于此,在Ather和Lenstra有关研究的基础上,利用初等方法给出了一个比较简洁的解答。

In 251 BC,Archimedes raised a cattle problem of the God of the Sun,which is still a hot issue in mathematical research.The research work on the issue has developed elementary number theory and algebraic number theory,and there are a lot of meaningful results on the issue.In this paper,based on the results of Ather and Lenstra,by the elementary methods,a more concise answer on the anantiquity issue is obtained.