题目:
Problem Description
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)=5x13+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”.
Input
The input contains several test cases. Each test case consists of a nonegative integer k, More details in the Sample Input.
Output
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.
Sample Input
11
100
9999
Sample Output
22
no
43
题意:给定一个方程式f(x)=5x13+13*x5+kax,给定一个非负整数k,求能不能找到一个尽量小的非负整数a,使得上述方程式中的x任意取值,结果都能被65整除,如果有,输出a的值,否则输出no。
数学题:F(0)=0,能被65整除。f(1) = 18+ka,要是让f(1)也满足题目要求的条件,则18+6ka就能被65整除
假设18+6ka=i, a = (i65-18)/k;利用循环,带入不同的i来求a。
代码:
//
// main.cpp
// hdu1098
//
// Created by zhan_even on 2018/10/31.
// Copyright © 2018年 zhan_even. All rights reserved.
//
#include <iostream>
using namespace std;
int main(int argc, const char * argv[]) {
int k,a;
while (cin>>k) {
a = 0;
for(int i=1;i<10000;i++){
if ((i*65-18)%k == 0) {
a = (i*65-18)/k;
break;
}
}
if (a==0) {
cout<<"no"<<endl;
}
else
cout<<a<<endl;
}
return 0;
}