## Diophantine reciprocals III

### Problem 454

In the following equation `x`, `y`, and `n` are positive integers.

1 x |
+ | 1 y |
= | 1 n |

For a limit `L` we define F(`L`) as the number of solutions which satisfy `x` < `y` ≤ `L`.

We can verify that F(15) = 4 and F(1000) = 1069.

Find F(10^{12}).