论文标题
$ \ mathbb {z} _ {n} $及其图表表示
gcd-Pairs in $\mathbb{Z}_{n}$ and their graph representations
论文作者
论文摘要
这项研究介绍了$ \ mathbb {z} _n $中的GCD-pair，这是一个无序的一对$ \ {[a] _n，[b] _n \} $ y Mathbb {z} _n $中的元素，$ 0 \ leq leq a，b <n $ and b <n $ and b <n $ and b n $ n $ n $ n b）研究了$ \ mathbb {z} _n $中GCD对的属性及其图表。我们还提供了$ \ mathbb {z} _n $及其子集的GCD对的计数公式。包括$ \ mathbb {z} _ {n} $中查找，计数和检查GCD对的算法。
This research introduces a gcd-pair in $\mathbb{Z}_n$ which is an unordered pair $\{[a]_n, [b]_n\}$ of elements in $ \mathbb{Z}_n $ such that $0\leq a,b < n$ and the greatest common divisor $\gcd(a,b)$ divides $ n $. The properties of gcd-pairs in $ \mathbb{Z}_n $ and their graph representations are investigated. We also provide the counting formula of gcd-pairs in $ \mathbb{Z}_n $ and its subsets. The algorithms to find, count and check gcd-pairs in $ \mathbb{Z}_{n}$ are included.
