可用于分解大费马数的算法

e Informatica Softw. Eng. J. Pub Date : 2020-05-01 DOI:10.17706/jsw.15.3.86-97

Xingbo Wang

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引用次数: 5

摘要

证明了如果N有一个2u +1或2u-1形式的除数，且>1为正整数，u>1为奇数，则奇数复合整数N最多可被分解为O(0.125u (log2N))个搜索步骤。用详细的数学推理证明了定理和推论。设计了一类奇合数的因式分解算法，并在一定的费马数下进行了测试。本文的结果可能对某些大费马数的因式分解有所帮助。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Algorithm Available for Factoring Big Fermat Numbers

The paper proves that an odd composite integer N can be factorized in at most O( 0.125u (log2N)) searching steps if N has a divisor of the form 2u +1 or 2u-1 with  >1 being a positive integer and u>1 being an odd integer. Theorems and corollaries are proved with detail mathematical reasoning. Algorithms to factorize the kind of odd composite integers are designed and tested with certain Fermat numbers. The results in the paper might be helpful to factorize certain big Fermat numbers.

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e Informatica Softw. Eng. J.

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