Online JudgeProblem SetAuthorsOnline ContestsUser
Web Board
Home Page
F.A.Qs
Statistical Charts
Problems
Submit Problem
Online Status
Prob.ID:
Register
Update your info
Authors ranklist
Current Contest
Past Contests
Scheduled Contests
Award Contest
User ID:
Password:
  Register

Re:求解10^x = 1 (mod 9*L/gcd(L,8))的满足x>0的最小解就是答案_证明内详

Posted by majia5 at 2010-06-04 10:26:51 on Problem 3696
In Reply To:Re:求解10^x = 1 (mod 9*L/gcd(L,8))的满足x>0的最小解就是答案_证明内详 Posted by:tanyin at 2009-08-07 16:35:05
>   刚刚弄错了。。。我对这个兄弟的解题过程有点迷糊。。
> 欧拉公式不是: a^phi(m) = 1 mode(m)吗?
> 看他一个举例:
> 
>      比如:L=11;9L/gcd(L,8)=99;phi(9L/gcd(L,8))=60;解得10^2 =1 (mod 99),2是满足条件的最小的因子了
>  
> 明明 phi(9L/gcd(L,8))=60 , 怎么就来了句“  10^2 =1 (mod 99),2是满足条件的最小的因子了”   按他的解题思路应该是60才对。。
>    
>    小生数论还没入门,请大牛们多多指教。。。


10^60 = 1 (mod 99)
可是对于60的所有因子,可以发现2是满足方程的,由于题目是需要求的最小,所以答案是2

Followed by:

Post your reply here:
User ID:
Password:
Title:

Content:

Home Page   Go Back  To top


All Rights Reserved 2003-2013 Ying Fuchen,Xu Pengcheng,Xie Di
Any problem, Please Contact Administrator