由于pcrazyc斑竹临时有事情.这期还是由我来出题目.希望大家继续支持.
第一题:
k尾相等数
Time Limit:1000MS Memory Limit:10000K
Description:
从键盘上输入一个整数k(k>1),若存在整数m,n(m>n),使得pow(k,m)和pow(k,n)均大于或等于1000，且末尾3位数相等，则称m和n是一对"k尾相等数"。请编写一程序求m+n值最小的k尾相等数。
input:
每行输入一个整数k;
output:
输出相应的最小m+n值;
sample input:
2
sample output
120
第二题:
Lagrange's Four-Square Theorem
Time Limit:1000MS Memory Limit:30000K
Total Submit:790 Accepted:339
Description
The fact that any positive integer has a representation as the sum of at most four positive squares (i.e. squares of positive integers) is known as Lagrange's Four-Square Theorem. The first published proof of the theorem was given by Joseph-Louis Lagrange in 1770. Your mission however is not to explain the original proof nor to discover a new proof but to show that the theorem holds for some specific numbers by counting how many such possible representations there are.
For a given positive integer n, you should report the number of all representations of n as the sum of at most four positive squares. The order of addition does not matter, e.g. you should consider 4^2 + 3^2 and 3^2 + 4^2 are the same representation.
For example, let's check the case of 25. This integer has just three representations 1^2+2^2+2^2+4^2, 3^2 + 4^2, and 5^2. Thus you should report 3 in this case. Be careful not to count 4^2 + 3^2 and 3^2 + 4^2 separately.
Input
The input is composed of at most 255 lines, each containing a single positive integer less than 2^15, followed by a line containing a single zero. The last line is not a part of the input data.
Output
The output should be composed of lines, each containing a single integer. No other characters should appear in the output.
The output integer corresponding to the input integer n is the number of all representations of n as the sum of at most four positive squares.
Sample Input
1
25
2003
211
20007
0
Sample Output
1
3
48
7
738
最后祝大家过一个愉快而又充实的五一!!!
简单翻译一下第二个:
就是把任意数字分解成不超过四个数字的平方和。{注意看紫色部分的例子说明}
问有多少种分法
[此贴子已经被作者于2007-4-27 17:08:31编辑过]
