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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  .

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Here is another way to see this.

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

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This shows the same thing.

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

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

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