freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-108-diophantine-rec...

---
id: 5900f3d91000cf542c50feeb
title: 'Problem 108: Diophantine Reciprocals I'
challengeType: 5
forumTopicId: 301732
---

# --description--

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

1/`x` + 1/`y` = 1/`n`

For `n` = 4 there are exactly three distinct solutions:

1/5 + 1/20 = 1/4  
1/6 + 1/12 = 1/4  
1/8 + 1/8 = 1/4

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
```
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00			`---`
			`id: 5900f3d91000cf542c50feeb`
			`title: 'Problem 108: Diophantine Reciprocals I'`
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`challengeType: 5`
fix(curriculum): Added forumTopicId to remaining 1200 challeng… (#36558) 2019-08-05 16:17:33 +00:00			`forumTopicId: 301732`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00			`---`

Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`# --description--`

feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00			`In the following equation x, y, and n are positive integers.`

Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			1/`x` + 1/`y` = 1/`n`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			For `n` = 4 there are exactly three distinct solutions:
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`1/5 + 1/20 = 1/4`
			`1/6 + 1/12 = 1/4`
			`1/8 + 1/8 = 1/4`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			What is the least value of `n` for which the number of distinct solutions exceeds one-thousand?
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`# --hints--`

			`diophantineOne()` should return 180180.
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			```js
			`assert.strictEqual(diophantineOne(), 180180);`
			```
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`# --seed--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`## --seed-contents--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
			```js
			`function diophantineOne() {`
fix: remove Good luck! comment from challenge seed code (#39575) 2020-09-15 16:57:40 +00:00
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00			`return true;`
			`}`

			`diophantineOne();`
			```

Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`# --solutions--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
			```js
			`// solution required`
			```