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T3 Tree and Its Traits in Understanding Integers

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Document pages: 14 pages

Abstract: Valuated binary tree is emerging its magicalcharacteristics in study of integers. As the father tree of all valuated binarysubtrees, T3 tree plays avery important role in studying the odd integers for its owning both the commonproperties of a general valuated binary tree and its own traits of covering allthe odd integers bigger than 1. The article investigates the properties of the T3 tree as well as themultiplications on the tree. It exhibits the distribution of a node smultiples, the distribution of the product of two nodes and the distribution ofthe square of a node. Some other contents such as fundamental properties of the T3 tree and pathconnecting a product to its divisor-nodes are also investigated with detailmathematical proofs. The theorems and corollaries proved in the article lay afoundation for future work.

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