## Diophantine reciprocals I

### Problem 108

Published on Friday, 4th November 2005, 06:00 pm; Solved by 8159; Difficulty rating: 30%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.