79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
58 lines
1.2 KiB
Markdown
58 lines
1.2 KiB
Markdown
---
|
|
id: 5900f3b21000cf542c50fec5
|
|
challengeType: 5
|
|
title: 'Problem 70: Totient permutation'
|
|
---
|
|
|
|
## Description
|
|
<section id='description'>
|
|
Euler's Totient function, φ(n) [sometimes called the phi function], is used to determine the number of positive numbers less than or equal to n which are relatively prime to n. For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and relatively prime to nine, φ(9)=6.The number 1 is considered to be relatively prime to every positive number, so φ(1)=1.
|
|
Interestingly, φ(87109)=79180, and it can be seen that 87109 is a permutation of 79180.
|
|
Find the value of n, 1 < n < 107, for which φ(n) is a permutation of n and the ratio n/φ(n) produces a minimum.
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>euler70()</code> should return 8319823.
|
|
testString: assert.strictEqual(euler70(), 8319823, '<code>euler70()</code> should return 8319823.');
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function euler70() {
|
|
// Good luck!
|
|
return true;
|
|
}
|
|
|
|
euler70();
|
|
```
|
|
|
|
</div>
|
|
|
|
|
|
|
|
</section>
|
|
|
|
## Solution
|
|
<section id='solution'>
|
|
|
|
```js
|
|
// solution required
|
|
```
|
|
</section>
|