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1126: Problem B: Discrete Logging

发表于 2017-10-06   |   分类于 HUSTOJ   |   阅读次数 1,207

题目描述

Problem B: Discrete Logging
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)

Read several lines of input, each containing P,B,N separated by a space, and for each line print the logarithm on a separate line. If there are several, print the smallest; if there is none, print "no solution".
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) .

输入

暂无

输出

暂无

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

参考代码

暂无

解析

暂无

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若是凉夜已成梦

若是凉夜已成梦

青春里 总有些事情要努力去做 总有些梦想要拼命去追。

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