C# - I wouldn't name it hard...

private static int[] quads = new int[498].AsEnumerable().Select((n, i) => 4 * (i + 1) * (i + 1)).ToArray();
private static int GCD(int a, int b)
{
    return a == 0 ? b : GCD(b % a, a);
}
private static bool contains(int div)
{
    int left = 0, right = 497;
    do
    {
        if (quads[left] == div || quads[right] == div) return true;
        int mid = (left + right) / 2;
        if (quads[mid] < div) left = mid;
        else right = mid;
    }
    while (left < right - 1);
    return quads[left] == div || quads[right] == div;
}
private static int getDivs(int n, out int evn)
{
    int cnt = 1;
    evn = 0;
    for (int i = 2; i <= (int)Math.Sqrt(n); i++)
    {
        if (n % i == 0)
        {
            cnt += n / i == i ? 1 : 2;
            if(contains(i)) evn++;
            if(n / i != i && contains(n/i)) evn++;
        }
    }
    return cnt;
}
public static string solveEvenQuadDiv(int n)
{
    if (n < 8 || n % 4 != 0) return "0";
    int tot = getDivs(n, out int evn);
    int gcd = GCD(evn, tot);
    return $"{evn/gcd}/{tot/gcd}";
}

...though some guess is required