---
id: 5900f3db1000cf542c50feed
title: 'Problem 110: Diophantine Reciprocals II'
challengeType: 5
forumTopicId: 301735
dashedName: problem-110-diophantine-reciprocals-ii
---

# --description--

In the following equation x, y, and n are positive integers.

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

It can be verified that when `n` = 1260 there are 113 distinct solutions and this is the least value of `n` for which the total number of distinct solutions exceeds one hundred.

What is the least value of `n` for which the number of distinct solutions exceeds four million?

**Note:** This problem is a much more difficult version of Problem 108 and as it is well beyond the limitations of a brute force approach it requires a clever implementation.

# --hints--

`diophantineTwo()` should return `9350130049860600`.

```js
assert.strictEqual(diophantineTwo(), 9350130049860600);
```

# --seed--

## --seed-contents--

```js
function diophantineTwo() {

  return true;
}

diophantineTwo();
```

# --solutions--

```js
// solution required
```