freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-70-totient-permutation.english.md

---
id: 5900f3b21000cf542c50fec5
challengeType: 5
title: 'Problem 70: Totient permutation'
forumTopicId: 302183
---

## Description
<section id='description'>

Euler's Totient function, φ(<var>n</var>) [sometimes called the phi function], is used to determine the number of positive numbers less than or equal to <var>n</var> which are relatively prime to <var>n</var>. 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 <var>n</var>, 1 < <var>n</var> < 10<sup>7</sup>, for which φ(<var>n</var>) is a permutation of <var>n</var> and the ratio <var>n</var>/φ(<var>n</var>) produces a minimum.

</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>totientPermutation()</code> should return a number.
    testString: assert(typeof totientPermutation() === 'number');
  - text: <code>totientPermutation()</code> should return 8319823.
    testString: assert.strictEqual(totientPermutation(), 8319823);

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function totientPermutation() {

  return true;
}

totientPermutation();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>