学术报告
【学术报告】Relative Class Number Condition on the Nagell-Ljunggren Equation
编辑:刘梦洁发布时间:2023年11月02日

报告人:陈汉(德国哥廷根大学)

间:202311515:30

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.

人简介

陈汉,厦门大学学士,厦门大学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。


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