HDU 1017 A Mathematical Curiosity

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本文介绍了一道关于寻找整数对(a, b)的数学题目，条件为0<a<b<n且(a²+b²+m)/(ab)为整数。通过给出的示例输入输出和源代码，展示了如何使用C语言解决该问题，包括读取多组测试数据和逐个案例的输出。

A Mathematical Curiosity

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 17014 Accepted Submission(s): 5299

Problem Description

Given two integers n and m, count the number of pairs of integers (a,b) such that 0 < a < b < n and (a^2+b^2 +m)/(ab) is an integer.

This problem contains multiple test cases!

The first line of a multiple input is an integer N, then a blank line followed by N input blocks. Each input block is in the format indicated in the problem description. There is a blank line between input blocks.

The output format consists of N output blocks. There is a blank line between output blocks.

Input

You will be given a number of cases in the input. Each case is specified by a line containing the integers n and m. The end of input is indicated by a case in which n = m = 0. You may assume that 0 < n <= 100.

Output

For each case, print the case number as well as the number of pairs (a,b) satisfying the given property. Print the output for each case on one line in the format as shown below.

Sample Input

Sample Output

  
   Case 1: 2
Case 2: 4
Case 3: 5

Source

East Central North America 1999, Practice

Recommend

JGShining

分析：简单题，注意b比a大即可

代码：

#include<stdio.h>

int main()
{
    int T;
    scanf("%d",&T);
    int m,n;
    while(T--)
    {
        int count=0;
        while(scanf("%d%d",&n,&m))
        {
            count++;
            int num=0;
            if(n==0&&m==0)
            break;
            int i,j;
            for(i=1;i<n;i++)
              for(j=i+1;j<n;j++)
              {
                  if((i*i+j*j+m)%(i*j)==0)
                      num++;
              }
              printf("Case %d: %d\n",count,num);
        }
        if(T!=0)
        printf("\n");
    }
    return 0;
}