计算物理 ›› 1988, Vol. 5 ›› Issue (1): 27-35.

• 论文 • 上一篇    下一篇

模M之m阶单位根的计数与确定

李凤林   

  1. 中国科学院计算中心
  • 收稿日期:1987-10-03 出版日期:1988-03-25 发布日期:1988-03-25

THE COUNT AND DETERMINATION OF M ORDERS UNIT ROOT FOR MODUL M

Li Feng-lin   

  1. Computing Center, Academia Sinica
  • Received:1987-10-03 Online:1988-03-25 Published:1988-03-25

摘要: 要根据[1]中给出的MCS序列xnαxn-1(modM)具有周期m的充要条件,确定其相应全部参数α,可归结为模Mm阶单位根的计数与确定问题,而此问题对一般复合模M至今未见解决。本文解决了这个问题,从而也解决了MCS序列具有周期m的全部参数α的计数和确定问题。

Abstract: In this paper, the method to determine all parameters a for MCS(xnΞaxn-1(modM),n ≥ 1) with any Period m is given on the basis of the theorems in[1] We deduce the parameters a from seeking m orders unit root for modul M' (M'=M/d, (x0,M)=d)and propose the simplified algorithms to do so for the composite m. A numerical example shows the correctness of the method.