OpenJudge

019:Discrete Logging

总时间限制:
5000ms
内存限制:
65536kB
描述
Given a prime P, 2 <= P < 231, an integer B, 2 <= B < P, and an integer N, 2 <= N < P, compute the discrete logarithm of N, base B, modulo P. That is, find an integer L such that
    BL == N (mod P)
输入
Read several lines of input, each containing P,B,N separated by a space.
输出
For each line print the logarithm on a separate line. If there are several, print the smallest; if there is none, print "no solution".
样例输入
5 2 1
5 2 2
5 2 3
5 2 4
5 3 1
5 3 2
5 3 3
5 3 4
5 4 1
5 4 2
5 4 3
5 4 4
12345701 2 1111111
1111111121 65537 1111111111
样例输出
0
1
3
2
0
3
1
2
0
no solution
no solution
1
9584351
462803587
提示
The solution to this problem requires a well known result in number theory that is probably expected of you for Putnam but not ACM competitions. It is Fermat's theorem that states
   B(P-1) == 1 (mod P)

for any prime P and some other (fairly rare) numbers known as base-B pseudoprimes. A rarer subset of the base-B pseudoprimes, known as Carmichael numbers, are pseudoprimes for every base between 2 and P-1. A corollary to Fermat's theorem is that for any m
   B(-m) == B(P-1-m) (mod P) .
来源
Waterloo Local 2002.01.26
全局题号
1419
添加于
2017-08-27
提交次数
0
尝试人数
0
通过人数
0