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good

Posted by frkstyc at 2005-12-07 19:11:45 on Problem 2720
In Reply To:Re:终于找到正确方法了. Posted by:zhucheng at 2005-12-07 17:31:18
> 只需要解决a^m mod n怎么计算,m非常大。
> 1)如果d=gcd(a,n)等于1,那么由欧拉定理得到原式等于a^(m mod Euler(n)) mod n
> Euler()是欧拉函数;
> 2)d不等于1,那么原式等于((a/d)^m*d*d^(m-1)) mod n
> ---> ((a/d)^m*d  mod n ) * ( d^(m-1) mod n) 
> ---->d*((a/d)^m mod (n/d)) *  (d^(m-2) mod (n/d))*d
> 分成两部分进行计算 
> d*((a/d)^m mod (n/d)) 可以用1)解决,因为 a/d和n/d互质。
> (d^(m-2) mod (n/d))*d继续递归解决。
> 粗糙的实现会超时,需要一些细节上的优化

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