Lucas定理

For non-negative integers m and n and a prime p, the following congruence relation holds:

\binom{m}{n}\equiv\prod_{i=0}^k\binom{m_i}{n_i}\pmod p,

where

m=m_kp^k+m_{k-1}p^{k-1}+\cdots +m_1p+m_0,

and

n=n_kp^k+n_{k-1}p^{k-1}+\cdots +n_1p+n_0

are the base p expansions of m and n respectively.

 

 

 

 

posted @ 2012-08-08 22:09  AC_Von  阅读(295)  评论(0)  编辑  收藏  举报