60 lines
1.4 KiB
Markdown
60 lines
1.4 KiB
Markdown
|
---
|
|||
|
id: 5900f3ee1000cf542c50ff00
|
|||
|
challengeType: 5
|
|||
|
title: 'Problem 130: Composites with prime repunit property'
|
|||
|
---
|
|||
|
|
|||
|
## Description
|
|||
|
<section id='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.
|
|||
|
You are given that for all primes, p > 5, that p − 1 is divisible by A(p). For example, when p = 41, A(41) = 5, and 40 is divisible by 5.
|
|||
|
However, there are rare composite values for which this is also true; the first five examples being 91, 259, 451, 481, and 703.
|
|||
|
Find the sum of the first twenty-five composite values of n for whichGCD(n, 10) = 1 and n − 1 is divisible by A(n).
|
|||
|
</section>
|
|||
|
|
|||
|
## Instructions
|
|||
|
<section id='instructions'>
|
|||
|
|
|||
|
</section>
|
|||
|
|
|||
|
## Tests
|
|||
|
<section id='tests'>
|
|||
|
|
|||
|
```yml
|
|||
|
tests:
|
|||
|
- text: <code>euler130()</code> should return 149253.
|
|||
|
testString: 'assert.strictEqual(euler130(), 149253, ''<code>euler130()</code> should return 149253.'');'
|
|||
|
|
|||
|
```
|
|||
|
|
|||
|
</section>
|
|||
|
|
|||
|
## Challenge Seed
|
|||
|
<section id='challengeSeed'>
|
|||
|
|
|||
|
<div id='js-seed'>
|
|||
|
|
|||
|
```js
|
|||
|
function euler130() {
|
|||
|
// Good luck!
|
|||
|
return true;
|
|||
|
}
|
|||
|
|
|||
|
euler130();
|
|||
|
```
|
|||
|
|
|||
|
</div>
|
|||
|
|
|||
|
|
|||
|
|
|||
|
</section>
|
|||
|
|
|||
|
## Solution
|
|||
|
<section id='solution'>
|
|||
|
|
|||
|
```js
|
|||
|
// solution required
|
|||
|
```
|
|||
|
</section>
|