---
id: 5900f3d91000cf542c50feeb
title: 'Problem 108: Diophantine Reciprocals I'
challengeType: 5
forumTopicId: 301732
dashedName: 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?

# --hints--

`diophantineOne()` should return 180180.

```js
assert.strictEqual(diophantineOne(), 180180);
```

# --seed--

## --seed-contents--

```js
function diophantineOne() {

  return true;
}

diophantineOne();
```

# --solutions--

```js
// solution required
```