Valuated binary tree is emerging its magical characteristics in study of integers. As the father tree of all valuated binary subtrees, T3 tree plays a very important role in studying the odd integers for its owning bo...Valuated binary tree is emerging its magical characteristics in study of integers. As the father tree of all valuated binary subtrees, T3 tree plays a very important role in studying the odd integers for its owning both the common properties of a general valuated binary tree and its own traits of covering all the odd integers bigger than 1. The article investigates the properties of the T3 tree as well as the multiplications on the tree. It exhibits the distribution of a node's multiples, the distribution of the product of two nodes and the distribution of the square of a node. Some other contents such as fundamental properties of the T3 tree and path connecting a product to its divisor-nodes are also investigated with detail mathematical proofs. The theorems and corollaries proved in the article lay a foundation for future work.展开更多
文摘Valuated binary tree is emerging its magical characteristics in study of integers. As the father tree of all valuated binary subtrees, T3 tree plays a very important role in studying the odd integers for its owning both the common properties of a general valuated binary tree and its own traits of covering all the odd integers bigger than 1. The article investigates the properties of the T3 tree as well as the multiplications on the tree. It exhibits the distribution of a node's multiples, the distribution of the product of two nodes and the distribution of the square of a node. Some other contents such as fundamental properties of the T3 tree and path connecting a product to its divisor-nodes are also investigated with detail mathematical proofs. The theorems and corollaries proved in the article lay a foundation for future work.
