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---
id: 5900f3db1000cf542c50feed
title: 'Problem 110: Diophantine Reciprocals II'
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challengeType: 5
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forumTopicId: 301735
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dashedName: problem-110-diophantine-reciprocals-ii
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---
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# --description--
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In the following equation x, y, and n are positive integers.
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$$\frac{1}{x} + \frac{1}{y} = \frac{1}{n}$$
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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.
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What is the least value of `n` for which the number of distinct solutions exceeds four million?
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**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.
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# --hints--
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`diophantineTwo()` should return `9350130049860600` .
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```js
assert.strictEqual(diophantineTwo(), 9350130049860600);
```
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# --seed--
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## --seed-contents--
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```js
function diophantineTwo() {
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return true;
}
diophantineTwo();
```
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# --solutions--
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```js
// solution required
```
