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Influence of Divisor-ratio to Distribution of Semiprime's Divisor

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  • Xingbo WANG

Abstract

For a semiprime that consists in two distinct odd prime divisors, this article makes an investigation on the distribution of the small divisor by analyzing the divisor-ratio that is calculated by the big divisor divided by the small one. It proves that, the small divisor must be a divisor of an odd integer lying in an interval that is uniquely determined by the divisor-ratio, and the length of the interval decreases exponentially with the increment of the ratio. Accordingly, a big divisor-ratio means the small divisor can be found in a small interval whereas a small divisor-ratio means it has to find the small divisor in a large interval. The proved theorems and corollaries can provide certain theoretical supports for finding out the small divisor of the semiprime.

Suggested Citation

  • Xingbo WANG, 2018. "Influence of Divisor-ratio to Distribution of Semiprime's Divisor," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 10(4), pages 54-61, August.
  • Handle: RePEc:ibn:jmrjnl:v:10:y:2018:i:4:p:54
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    More about this item

    Keywords

    Semiprime; divisor-ratio; distribution law;
    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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