Problem 9-Project Euter

A Pythagorean triplet is a set of three natural numbers, a b c, for which,

a² + b² = c²

For example, 3² + 4² = 9 + 16 = 25 = 5².

There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc.

//通项公式
//a=M^2-N^2 　　
//b=2MN
//c=M^2+N^2 
//（M,N为正整数）
int main()
{
    int a,b,c;

    int flag=0;
    for(int M=3;M<=33;M++)
    {
        for(int N=3;N<M;N++)
        {
            a=M*M-N*N;
            b=2*M*N;
            c=M*M+N*N;
            if(a+b+c==1000) {flag=1;break;}
        }
        if(flag==1) break;
    }
    printf("%d,%d,%d",a,b,c);
    printf("%d",a*b*c);
    return 0;
}

 

Answer:

31875000