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

## Description
<section id='description'>
In the following equation x, y, and n are positive integers.
1/<var>x</var> + 1/<var>y</var> = 1/<var>n</var>
For <var>n</var> = 4 there are exactly three distinct solutions:
1/5 + 1/20 = 1/4<br />1/6 + 1/12 = 1/4<br />1/8 + 1/8 = 1/4
What is the least value of <var>n</var> for which the number of distinct solutions exceeds one-thousand?
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>diophantineOne()</code> should return 180180.
    testString: assert.strictEqual(diophantineOne(), 180180);

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function diophantineOne() {
  // Good luck!
  return true;
}

diophantineOne();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>