---
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.

$$\frac{1}{x} + \frac{1}{y} = \frac{1}{n}$$

For `n` = 4 there are exactly three distinct solutions:

$$\begin{align}
  & \frac{1}{5} + \frac{1}{20} = \frac{1}{4}\\\\
  \\\\
  & \frac{1}{6} + \frac{1}{12} = \frac{1}{4}\\\\
  \\\\
  & \frac{1}{8} + \frac{1}{8} = \frac{1}{4}
\end{align}$$

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
```