[code source] score split of one question per day

Topic link ： Fraction split - subject - Daimayuan Online Judge

Title Description ：

Enter a positive integer k, Find all positive integers y≤x, bring 1/k=1/x+1/y.

Input format

Enter a positive integer k(1≤k≤10^7).

Output format

Output a number , That satisfies the condition x,y The number of .

The sample input

12

Sample output

8

because k The scope is very large, corresponding to x,y The value may also be very large , If violence enumeration will undoubtedly timeout , Then let's consider narrowing the scope of enumeration .

given k,x,y The relationship between ,k It is known that , Yes x,y When we know one term, we can push it to another term by equation . According to y<=x, You can get y<=2k, also y>k. From the equation, we can get x=(ky)/(y-k).

Code ：

#include <bits/stdc++.h>
using namespace std;
#define ll long long
ll cnt, k, ans;
int main()
{
    cin >> k;
    for (ll y = k + 1; y <= k + k; y++)
    {
        if ((k * y) % (y - k) == 0)
            ans++;
    }
    cout << ans;
}