Mathematica 9 is now available

MultiplicativeOrder

Usage

MultiplicativeOrder[k, n] 给出以 n 为模的k的乘法阶数, 定义为使得  成立的最小整数 .
MultiplicativeOrder[k, n,   ,  , ...  ]给出以 n 为模的k的广义乘法阶数,定义为使得 成立的最小整数 .


Notes

• 整型数学函数 (参见 A.3.10节).
• 若不存在整数 满足必要条件,则MultiplicativeOrder不进行计算就返回.
• 参见 Mathematica 全书: 3.2.4节.
Further Examples

The  in the fourth place shows that  is the least m for which  divides  .

In[1]:=  

Out[1]=

Here is another way to see this.

In[2]:=  

Out[2]=

This shows that  is the smallest integer m such that  is congruent to  or  mod  .

In[3]:=  

Out[3]=

This shows the same thing.

In[4]:=  

Out[4]=

The function DigitCycleLength gives the digit period for any rational number r in base b.

In[5]:=  

This shows that the decimal representation of  in base  repeats every  digits.

In[6]:=  

Out[6]=

In[7]:=  

Out[7]=

In[8]:=  



Any questions about topics on this page? Click here to get an individual response.Buy NowMore Information
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.