913 B
913 B
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f3d91000cf542c50feeb | Problem 108: Diophantine Reciprocals I | 5 | 301732 | 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
```