Ignatius's puzzle
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 4935 Accepted Submission(s): 3359
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".
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
Author
eddy
若对任意x成立,则当x=1时必然成立.若当x=1时成立,则对任意正整数x都成立.
观察题目中给出的式子可以看出每一项都有公因子x,所以f(x)必然是f(1)的x倍,若f(1)是65的倍数,则f(x)必然也是65的倍数.
#include<stdio.h>
int
main()
{
int
k;
while
(scanf(
"
%d
"
,&k)!=
EOF)
{
if
(k==
1
|| (k%
5
!=
0
&& k%
13
!=
0
&& k%
65
!=
0
))
{
for
(
int
i=
1
;;i++
)
if
((
18
+k*i)%
65
==
0
)
{
printf(
"
%d\n
"
,i);
break
;
}
}
else
printf(
"
no\n
"
);
}
return
0
;
}
