53 lines
913 B
Markdown
53 lines
913 B
Markdown
---
|
|
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
|
|
```
|