【数学】Ignatius's puzzle

描述

Ignatius is poor at math,he falls across a puzzle problem,so he has no choice but to appeal to Eddy. this problem describes that:f(x)=5x^13+13*x5+ka*x,input a nonegative integer k(k<10000),to find the minimal nonegative integer a,make the arbitrary integer x ,65|f(x)if
no exists that a,then print “no”.

输入

The input contains several test cases. Each test case consists of a nonegative integer k, More details in the Sample Input.

输出

The output contains a string “no”,if you can’t find a,or you should output a line contains the a.More details in the Sample Output.

样例输入

11
100
9999

样例输出

22
no
43

题目来源

HDOJ

分析：
1、f(x)为65的倍数，知k求a 18+ka=65 满足18%gcd（k，65）=0
2、展开f(x+1)与f(x)处理。
代码：
#include<bits/stdc++.h>
using namespace std;
int gcd(int x,int y)
{
int z;
if (x<y) swap(x,y);
while(y>0)
{
z=y;
y=x%y;
x=z;
}
return z;
}
int main()
{
int k;
while(cin>>k)
{
if (18%gcd(k,65)==0)
{
for (int i=0;;i++)
{
int d=ik+18;
if (d%65==0)
{
cout<<i<<endl;
break;
}
}
}
else
cout<<“no”<<endl;
}
return 0;
}

来源：CSDN

作者：Skynamer

链接：https://blog.csdn.net/Skynamer/article/details/104135401