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

# --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--

`repunitDivisibility()` should return `1000023`.

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

# --seed--

## --seed-contents--

```js
function repunitDivisibility() {

  return true;
}

repunitDivisibility();
```

# --solutions--

```js
// solution required
```