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Factorization of Odd Integers as Lattice Search Procedure

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Computational Intelligence and Intelligent Systems (ISICA 2017)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 874))

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Abstract

The article puts forward a 3-dimensional searching approach that can factorize odd composite integers. The article first proves that, an odd composite number can be expressed by a trivariate function, then demonstrates that factorization of an odd integer can be turned into a problem of searching a point in a 3-dimensional cube whose points can be searched rapidly via octree search algorithm or other 3-dimensional searching algorithm. Mathematical principles with their proofs are presented in detail, and an algorithm that reaches square of logarithm time-complexity is proposed with numerical examples. The proposed algorithm can be applied both in sequential computation and parallel computation.

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Acknowledgment

The research work is supported by Department of Guangdong Science and Technology[grant number 2015A030401105 and 2015A010104011]; the State Key Laboratory of Mathematical Engineering and Advanced Computing[grant number 2017A01]; Foshan Bureau of Science and Technology [grant number 2016AG100311]; Foshan University[grant number gg040981]. The authors sincerely present thanks to them all. The authors sincerely present thanks to them all.

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Authors and Affiliations

  1. Foshan University, Foshan City, 528000, Guangdong Province, People’s Republic of China

    Xingbo Wang

  2. State Key Laboratory of Mathematical Engineering and Advanced Computing, Wuxi, China

    Xingbo Wang

Authors
  1. Xingbo Wang
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Correspondence to Xingbo Wang .

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Editors and Affiliations

  1. College of Mathematics and Informatics, South China Agricultural University, Guangzhou, China

    Kangshun Li

  2. Jiangxi University of Science and Technology, Ganzhou, Jiangxi, China

    Wei Li

  3. Chemical and Petroleum Engineering, University of Calgary, Calgary, Alberta, Canada

    Zhangxing Chen

  4. School of Computer Science and Engineering, The University of Aizu, Aizu-Wakamatsu, Fukushima, Japan

    Yong Liu

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Wang, X. (2018). Factorization of Odd Integers as Lattice Search Procedure. In: Li, K., Li, W., Chen, Z., Liu, Y. (eds) Computational Intelligence and Intelligent Systems. ISICA 2017. Communications in Computer and Information Science, vol 874. Springer, Singapore. https://doi.org/10.1007/978-981-13-1651-7_22

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  • DOI: https://doi.org/10.1007/978-981-13-1651-7_22

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-1650-0

  • Online ISBN: 978-981-13-1651-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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