---
id: 5900f3d91000cf542c50feeb
challengeType: 5
title: 'Problem 108: Diophantine Reciprocals I'
---
## Description
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?
## Instructions
## Tests
```yml
tests:
- text: diophantineOne() should return 180180.
testString: assert.strictEqual(diophantineOne(), 180180, 'diophantineOne() should return 180180.');
```
## Challenge Seed
```js
function diophantineOne() {
// Good luck!
return true;
}
diophantineOne();
```