## Diophantine reciprocals I

### Problem 108

Published on Friday, 4th November 2005, 06:00 pm; Solved by 6511

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

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

For n = 4 there are exactly three distinct solutions:

1 5 | + | 1 20 | = | 1 4
1 6 | + | 1 12 | = | 1 4
1 8 | + | 1 8 | = | 1 4

What is the least value of n for which the number of distinct solutions exceeds one-thousand?

NOTE: This problem is an easier version of problem 110; it is strongly advised that you solve this one first.