hdu5478 Can you find it（数学）

最新推荐文章于 2021-02-07 23:21:10 发布

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本文介绍了一种解决特定模数方程问题的方法，通过枚举变量a来求解b，进而验证n=2时方程是否成立。适用于给定素数C及参数k1、b1、k2的情形。

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思路：通过n=1的时候枚举a求出b，然后通过n=2的时候验证是否成立

#include<bits/stdc++.h>
using namespace std;
#define LL long long
LL C,k1,b1,k2;
LL qpow(LL x,LL n,LL mod)
{
    LL ans=1;
    while(n>0)    
    {
        if(n&1)    ans=(ans*x)%mod;
        x=(x*x)%mod;
        n>>=1;
    }
    return ans;
}
int main()
{
    int T,cas=1;
    while(scanf("%lld%lld%lld%lld",&C,&k1,&b1,&k2)!=EOF)
    {
        int flag = 0;
        printf("Case #%d:\n",cas++);
        for(LL a = 1;a<C;a++)
        {
            LL b = C-qpow(a,k1+b1,C);
            LL x = qpow(a,2*k1+b1,C);
            LL y = qpow(b,k2+1,C);
            if((x+y)%C==0)
            {
                printf("%lld %lld\n",a,b);
                flag = 1;
            }
        }
        if(!flag)
            printf("-1\n");
    }
}

Problem Description

Given a prime number

C(1≤C≤2×105) , and three integers k1, b1, k2

(1≤k1,k2,b1≤109) . Please find all pairs (a, b) which satisfied the equation

ak1⋅n+b1 +

bk2⋅n−k2+1 = 0 (mod C)(n = 1, 2, 3, ...).

Input

There are multiple test cases (no more than 30). For each test, a single line contains four integers C, k1, b1, k2.

Output

First, please output "Case #k: ", k is the number of test case. See sample output for more detail.
Please output all pairs (a, b) in lexicographical order.

(1≤a,b<C) . If there is not a pair (a, b), please output -1.

Sample Input