梅森数、瓦格斯塔夫数推广及其整数因子研究

Generalization and Divisible Integers of Mersenne Numbers and Wagstaff Numbers

将梅森数和瓦格斯塔夫数推广为Z_p和Q_p,给出了奇数整除Z_p和Q_p的充分必要条件,分别证明了任意两个Z_p互素、任意两个Q_p互素和任意Z_p和Q_p互素,得出了Z_p和Q_p素因子的表示形式,提出了确定性检测瓦格斯塔夫数是否为素数的猜想.

This paper generalizes Mersenne Numbers and Wagstaff Numbers into ZI, and Qp , gives suffi-cient and necessary conditions for odd numbers to divide Zp and Qp. It proves that any two are relatively prime toeach other. This rule could also be applied between any two Qp , as well as any Zp and Qp. This paper then leadout the forms of prime factors of Zp and Qp , proposes guesses of deterministic tests on whether Wagstaff numberscan be prime or not.