论文标题
规范形式方程和线性脱序序列
Norm Form Equations and Linear Divisibility Sequences
论文作者
论文摘要
找到通用形式方程的整数解决方案是一个经典的双志甘油问题。使用相关系数环的单元，我们可以为这些方程式产生解决方案序列。众所周知，这些溶液可以写成线性复发序列的元素。我们表明，对于某些在四分之一字段定义的规范形式的家族，存在整体等效的形式，使任何一个固定的坐标序列是线性划分序列。
Finding integer solutions to norm form equations is a classical Diophantine problem. Using the units of the associated coefficient ring, we can produce sequences of solutions to these equations. It is known that these solutions can be written as tuples of linear recurrence sequences. We show that for certain families of norm forms defined over quartic fields, there exist integrally equivalent forms making any one fixed coordinate sequence a linear divisibility sequence.
