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

Xingbo Wang

Journal of Mathematics Research, 2018, vol. 10, issue 4, 54-61

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.

Keywords: Semiprime; divisor-ratio; distribution law (search for similar items in EconPapers)
Date: 2018
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