Two Symmetric Properties of Mersenne Numbers and Fermat Numbers

2013/04/27 by Shi Yongjin, Yongjin, Shi
Mathematics · #FOS: Mathematics #General Mathematics (math.GM) #math.GM

paper · pdf · doi:10.48550/arxiv.1304.7321

10 pages, no figures

arxiv created 2013/05/09 · arxiv updated 2013/05/10

Abstract

Mersenne numbers and Fermat numbers are two hot and difficult issues in number theory. This paper constructs a special group for every positive odd number other than 1, and discovers an algorithm for determining the multiplicative order of 2 modulo q for each positive odd number q. It is worth mentioning that this paper discovers two symmetric properties of Mersenne numbers and Fermat numbers.

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