报告人：陈汉（德国哥廷根大学）

时 间：2023年11月5日15:30

地 点：海韵园数理大楼686会议室

内容摘要:

The Diophantine equation of Nagell-Ljunggren $\frac{x^{n}-1}{x-1}=y^{q} $ has six known solutions  $(x, y, n, q) \in   \{ (3, \pm 11, 5, 2),(7, \pm 20, 4, 2),(18, 7, 3, 3),(-19, 7, 3, 3) \} $ in integers $x, y, q$ and $n$ with $|x|, |y|, q>1$ and $n>2$. The Conjecture of Nagell and Ljunggren states that these are the only solutions in integers.  We show that, for $p > 3$, it has no positive solutions under the condition that $q$ does not divide $h_p^-$, the minus part of the class number of the $p$-th cyclotomic field.  This is a joint work with Preda Mihailescu.

个人简介：

陈汉，hg8868官方网站学士，hg8868官方网站和法国波尔多大学硕士，2023年获得德国哥廷根大学博士，主要研究领域是数论，特别是丢番图方程、丢番图逼近和代数数论等方面，目前已经在Chinese Annals of Mathematics Series B上接收发表论文。

联系人：祝辉林