hdu 1098 Ignatius's puzzle
題目:
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
題意:給定一個方程式f(x)=5x13+13*x5+kax,給定一個非負整數k,求能不能找到一個儘量小的非負整數a,使得上述方程式中的x任意取值,結果都能被65整除,如果有,輸出a的值,否則輸出no。
數學題:F(0)=0,能被65整除。f(1) = 18+ka,要是讓f(1)也滿足題目要求的條件,則18+6ka就能被65整除
假設18+6ka=i, a = (i65-18)/k;利用迴圈,帶入不同的i來求a。
程式碼:
// // 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; }