n+1/n = 1/x1 + 1/x2 + 1/x3，n为质数，1＜=x1,x2,x3＜=1000，求整数x1,x2,x3

需求描述

已知等式n+1/n = 1/x1 + 1/x2 + 1/x3，n为质数，1<=x1,x2,x3<=1000
求整数x1，x2，x3的值并按从小到大的顺序输出。

#include<iostream>
using namespace std;
int s[1000];
int flag=0;
bool isrepeat(int a,int b,int c)//判断a,b,c是否已重复存在于s[]中 
{
    
    
	int fly=0;
	for( int i=0; i<flag; i++ )
	{
    
    
		if( s[i] == a )
		fly++;
		if( s[i] == b )
		fly++;
		if( s[i] == c )
		fly++;
	}
	if( fly == 3 )
	return true;
	return false;
}
void save(int a,int b,int c)//保存a,b,c中不重复的值 
{
    
    
	int t1=0,t2=0,t3=0;
	for( int i=0; i<flag; i++ )
	{
    
    
		if( s[i] == a )
		t1=1;
		if( s[i] == b )
		t2=1;
		if( s[i] == c )
		t3=1;
	}
	if( !t1 )
	s[flag++] = a;
	if( a != b && !t2 )
	s[flag++] = b;
	if( a != c && b != c && !t3 )
	s[flag++] = c;
}
int main()
{
    
    
	/*  n+1/n = 1/x1 + 1/x2 + 1/x3  n为质数 1<=x1,x2,x3<=1000  */
	double n;//质数
	double x1,x2,x3;
	int y1,y2,y3;
	while( true )
	{
    
    
		cin>>n;
		for( x1=1 ; x1<=1000; x1++ )
		{
    
    
			for( x2= 1; x2<=1000; x2++ )
			{
    
    
				for( x3=1; x3<=1000; x3++ )
				{
    
    
					if( ( n+1 )*( x1*x2*x3 ) == n*( x1*x2 + x1*x3 + x2*x3 ) && !isrepeat(x1,x2,x3) )/*(n+1)/n==(1/x1+1/x2+1/x3)*/
					{
    
    
						cout<<"x1= "<<x1<<"  "<<"x2= "<<x2<<"  "<<"x3= "<<x3<<endl;
						save(x1,x2,x3);
					}
					if( (n+1)/n > (1/x1+1/x2+1/x3) )
					break;
				}
				
			}
			
		} 
		flag = 0;
		s[1000] = 0;
	}
	
	return 0;
}  

运行结果

2
x1= 1  x2= 3  x3= 6
x1= 1  x2= 4  x3= 4
x1= 2  x2= 2  x3= 2
3
x1= 1  x2= 4  x3= 12
x1= 1  x2= 6  x3= 6
x1= 2  x2= 2  x3= 3
5
x1= 1  x2= 6  x3= 30
x1= 1  x2= 10  x3= 10
x1= 2  x2= 2  x3= 5
7
x1= 1  x2= 8  x3= 56
x1= 1  x2= 14  x3= 14
x1= 2  x2= 2  x3= 7
11
x1= 1  x2= 12  x3= 132
x1= 1  x2= 22  x3= 22
x1= 2  x2= 2  x3= 11
13
x1= 1  x2= 14  x3= 182
x1= 1  x2= 26  x3= 26
x1= 2  x2= 2  x3= 13