Fibonacci Again
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 44035 Accepted Submission(s): 21020
Problem Description
There are another kind of Fibonacci numbers: F(0) = 7, F(1) = 11, F(n) = F(n-1) + F(n-2) (n>=2).
Input
Input consists of a sequence of lines, each containing an integer n. (n < 1,000,000).
Output
Print the word "yes" if 3 divide evenly into F(n).
Print the word "no" if not.
Print the word "no" if not.
Sample Input
0 1 2 3 4 5
Sample Output
no no yes no no no
http://acm.hdu.edu.cn/showproblem.php?pid=1021
先打出前50个的数的答案发现他有一种规律,要推得话也是可以的,7%3=1,11%3=2,那么(7+11)%3一定是0,后面余数分别是2,2,1,0,1,1,2,0.。。。。。。
so代码如下:
#include <cstdio>
int main()
{
int n;
while(scanf("%d",&n)!=EOF){
if(n==0||n==1)printf("no\n");
else if(n%4==2)printf("yes\n");
else printf("no\n");
}
return 0;
}
本文探讨了Fibonacci序列中3的除尽性规律,并通过编程实现验证。揭示了Fibonacci序列每四项之后3能整除一项的周期性现象。
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