---
id: 5900f52c1000cf542c51003e
challengeType: 5
title: 'Problem 447: Retractions C'
forumTopicId: 302119
---

## Description
<section id='description'>
For every integer n>1, the family of functions fn,a,b  is defined
by fn,a,b(x)≡ax+b mod n for a,b,x integer and  0<a<n, 0≤b<n, 0≤x<n.
We will call fn,a,b a retraction if fn,a,b(fn,a,b(x))≡fn,a,b(x) mod n for every 0≤x<n.
Let R(n) be the number of retractions for n.


F(N)=∑R(n) for 2≤n≤N.
F(107)≡638042271 (mod 1 000 000 007).


Find F(1014) (mod 1 000 000 007).
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler447()</code> should return 530553372.
    testString: assert.strictEqual(euler447(), 530553372);

```

</section>

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

<div id='js-seed'>

```js
function euler447() {

  return true;
}

euler447();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>