Lucas theorems of number theory summary

Number theory because I compare it to write their own understanding after the special dishes, so I read someone else's blog.

And the time of emergency, poor environment, so what's the formula I directly copied [So what's it as a variable name.

Lucas

  Lucas is used to solve some of the theorems number of combinations of the modulo operation, often it can not be resolved in time factorial we think ta.

  

  Before looking at Lucas implementation method, we first prove a thing.

  

  We just need him apart, below ↓ this place less of a "=" symbol

  

  QED.

  So we are going on the use of this property as well as the binomial theorem to push conclusion.

      Binomial theorem:

  You can easily get: [I push over as long as serious is certainly very evident

  

  So we are going to prove:

  

  We found only one left, and right there is a good number, so take it apart.

  We set .

  Then the above equation after transposition deformation, becomes this:

  We found that there is actually a picture-ta relationship problems, it can be solved recursively.

  OK, so we returned to the binomial theorem,

  Expand (. 1 + X) LP , to give the following things:

  

  A closer look at the relationship factor.

  

    ¤ employed herein is rounded down must pay attention.

  QED.

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Origin www.cnblogs.com/qxyzili--24/p/11229472.html