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Interval Tree and Its Application in Integer Factorization

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  • Xingbo WANG

Abstract

The paper first puts forward a way to study odd integers by placing the odd integers in a given interval on a perfect full binary tree, then makes an investigation on the odd integers by means of combining the original properties of the integers with the properties of the binary trees and obtains several new results on how an odd integer's divisors distribute on a level of a binary tree. The newly discovered law of divisors' distribution that includes common divisors between two symmetric nodes, genetic divisors between an ancestor node and its descendant node can provide a new and simple approach to factorize odd composite integers. Based on the mathematical deductions, numerical experiments are designed and demonstrated in the Maple software. All the results of the experiments are conformance to expectation and validate the validity of the approach.

Suggested Citation

  • Xingbo WANG, 2019. "Interval Tree and Its Application in Integer Factorization," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 11(2), pages 103-113, April.
    • Handle: RePEc:ibn:jmrjnl:v:11:y:2019:i:2:p:103
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    References listed on IDEAS

    as
    1. Xingbo WANG & Zhen SHEN, 2018. "Traits of a RSA Modulus on T3 Tree," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 10(6), pages 15-29, December.
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      More about this item

      Keywords

      binary tree; integer factorization; genetic trait; algorithm;
      All these keywords.

      JEL classification:

      • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
      • Z0 - Other Special Topics - - General

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