freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-129-repunit-divisibility.md

---
id: 5900f3ef1000cf542c50ff01
title: 'Problem 129: Repunit divisibility'
challengeType: 5
forumTopicId: 301756
---

# --description--

A number consisting entirely of ones is called a repunit. We shall define R(k) to be a repunit of length k; for example, R(6) = 111111.

Given that n is a positive integer and GCD(n, 10) = 1, it can be shown that there always exists a value, k, for which R(k) is divisible by n, and let A(n) be the least such value of k; for example, A(7) = 6 and A(41) = 5.

The least value of n for which A(n) first exceeds ten is 17.

Find the least value of n for which A(n) first exceeds one-million.

# --hints--

`euler129()` should return 1000023.

```js
assert.strictEqual(euler129(), 1000023);
```

# --seed--

## --seed-contents--

```js
function euler129() {

  return true;
}

euler129();
```

# --solutions--

```js
// solution required
```
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00			`---`
			`id: 5900f3ef1000cf542c50ff01`
			`title: 'Problem 129: Repunit divisibility'`
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: 301756`
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			`A number consisting entirely of ones is called a repunit. We shall define R(k) to be a repunit of length k; for example, R(6) = 111111.`
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00
feat(challenge-md): Add initial markdown challenge files 2018-09-30 23:01:58 +01:00			`Given that n is a positive integer and GCD(n, 10) = 1, it can be shown that there always exists a value, k, for which R(k) is divisible by n, and let A(n) be the least such value of k; for example, A(7) = 6 and A(41) = 5.`

Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 19:02:05 +01:00			`The least value of n for which A(n) first exceeds ten is 17.`
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			`Find the least value of n for which A(n) first exceeds one-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			`euler129()` should return 1000023.
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(euler129(), 1000023);`
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 euler129() {`
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;`
			`}`

			`euler129();`
			```

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`
			```