Project Euler 136

题目

Singleton difference

The positive integers, \(x, y\), and \(z\), are consecutive terms of an arithmetic progression. Given that \(n\) is a positive integer, the equation, \(x^2 − y^2 − z^2 = n\), has exactly one solution when \(n = 20\):

\[13^2 − 10^2 − 7^2 = 20\]

In fact there are twenty-five values of \(n\) below one hundred for which the equation has a unique solution.

How many values of \(n\) less than fifty million have exactly one solution?

解决方案

本题的解决方案和第135题完全一样，在这里不再赘述。

代码

# include <bits/stdc++.h>
using namespace std;
const int N=5e7,Q=1;
int c[N+4];
int main(){
    for(int z=1;z<=N;z++){
        for(int d=z/3+1;;d++){
            int w=(3*d-z)*(d+z);
            if(w>=N) break;
            c[w]+=1;
        }
    }
    int ans=0;
    for(int i=1;i<=N;i++)
        if(c[i]==Q) ++ans;
    printf("%d\n",ans);
}