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Diophantine reciprocals III

Problem 454 Published on Saturday, 11th January 2014, 07:00 pm; Solved by 343;
Difficulty rating: 50%

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 < yL.

We can verify that F(15) = 4 and F(1000) = 1069.
Find F(1012).