47 lines
1.0 KiB
Markdown
47 lines
1.0 KiB
Markdown
---
|
|
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
|
|
```
|