论文标题
在与Collatz猜想相关的轨道上
On the orbits associated with the Collatz conjecture
论文作者
论文摘要
本文基于Sousa Ramos及其合作者以前的工作。他们首先证明，仅与Collatz猜想相关的一个轨道的存在等效于某些矩阵序列的每个矩阵的决定符，以具有相同的值。这些矩阵称为Collatz矩阵。他们工作的第二步是计算每个Collatz矩阵的决定因素。在计算了矩阵序列序列的前几个术语的决定因素之后，他们的计划是证明当前项的决定因素等于上一项的决定因素。不幸的是，在矩阵的尺寸为26+54L或44+54L的情况下，它们无法证明这一点，其中L是正整数。在当前文章中，我们改进了这些结果。
This article is based upon previous work by Sousa Ramos and his collaborators. They first prove that the existence of only one orbit associated with the Collatz conjecture is equivalent to the determinant of each matrix of a certain sequence of matrices to have the same value. These matrices are called Collatz matrices. The second step in their work would be to calculate this determinant for each of the Collatz matrices. Having calculated this determinant for the first few terms of the sequence of matrices, their plan was to prove the determinant of the current term equals the determinant of the previous one. Unfortunately, they could not prove it for the cases where the dimensions of the matrices are 26+54l or 44+54l, where l is a positive integer. In the current article we improve on these results.
