freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-110-diophantine-reciprocals-ii.md

---
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.

1/`x` + 1/`y` = 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?

# --hints--

`diophantineTwo()` should return 9350130049860600.

```js
assert.strictEqual(diophantineTwo(), 9350130049860600);
```

# --seed--

## --seed-contents--

```js
function diophantineTwo() {

  return true;
}

diophantineTwo();
```

# --solutions--

```js
// solution required
```
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00			`---`
			`id: 5900f3db1000cf542c50feed`
			`title: 'Problem 110: Diophantine Reciprocals II'`
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`challengeType: 5`
fix(curriculum): Added forumTopicId to remaining 1200 challeng… (#36558) 2019-08-05 09:17:33 -07:00			`forumTopicId: 301735`
feat(curriculum): restore seed + solution to Chinese (#40683) * feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com> 2021-01-13 03:31:00 +01:00			`dashedName: problem-110-diophantine-reciprocals-ii`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00			`---`

Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`# --description--`

feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00			`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 19:02:05 +01:00			1/`x` + 1/`y` = 1/`n`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			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.
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			What is the least value of `n` for which the number of distinct solutions exceeds four million?
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`# --hints--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`diophantineTwo()` should return 9350130049860600.
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			```js
			`assert.strictEqual(diophantineTwo(), 9350130049860600);`
			```
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`# --seed--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`## --seed-contents--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
			```js
			`function diophantineTwo() {`
fix: remove Good luck! comment from challenge seed code (#39575) 2020-09-15 09:57:40 -07:00
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00			`return true;`
			`}`

			`diophantineTwo();`
			```

Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`# --solutions--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00
			```js
			`// solution required`
			```