doi: 10.17706/ijapm.2019.9.1.1-11
Some Divisibility Traits on Valuated Binary Trees
Xingbo Wang
,
- Department of Mechatronic Engineering, Foshan University, Foshan City, 528000, China.
Abstract
The paper investigates some divisibility traits on valuated binary trees, including some divisibility rules on <em>T</em><sub>3</sub> tree and some laws of multiples’ distribution on a <em>T<sub>p</sub></em> tree. It proves that the root of a valuated binary tree can always have a common divisor with certain nodes that appear periodically on the left most path or the left side-path of the tree and calculation of divisors of a node is highly related with the two’s power plus one and the two’s power minus one. Theorems and corollaries are proved with detail mathematical deductions and they provide a foundation for people to design algorithm for factoring odd integers.
Keywords
- Number theory
- integer factorization
- congruence equation
- binary tree
How to Cite
Xingbo Wang and Hongqiang Guo, "Some Divisibility Traits on Valuated Binary Trees," International Journal of Applied Physics and Mathematics, vol. 9, no. 1, pp. 1-11, 2019. https://doi.org/ 10.17706/ijapm.2019.9.1.1-11
Copyright & License
Copyright © 2019 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).