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.