Ignatius's puzzle
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)=5*x^13+13*x^5+k*a*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".
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
这道题目难点不在编程,在数学!数学归纳法证明! 最后只要证明 18 + k * a 能整除65就可以了。
代码:
#include<stdio.h> int main () { int a = 0; int k = 0; while ( scanf ( "%d" , &k ) != EOF ) { if ( k % 65 == 0 ) { printf ( "no\n" ) ; continue ; } for ( a = 1 ; a <= 65 ; ++ a ) { if ( ( 18 + k * a ) % 65 == 0 ) { printf ( "%d\n" , a ) ; break ; } } if ( a > 65 ) { printf ( "no\n" ) ; } } return 0 ; }