---
id: 5900f52c1000cf542c51003d
challengeType: 5
title: 'Problem 446: Retractions B'
---

## 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(n4+4) for 1≤n≤N.
F(1024)=77532377300600.

Find F(107) (mod 1 000 000 007)
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler446()</code> should return 907803852.
    testString: assert.strictEqual(euler446(), 907803852, '<code>euler446()</code> should return 907803852.');

```

</section>

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

<div id='js-seed'>

```js
function euler446() {
  // Good luck!
  return true;
}

euler446();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>