---
id: 5900f52c1000cf542c51003e
title: 'Problem 447: Retractions C'
challengeType: 5
forumTopicId: 302119
dashedName: problem-447-retractions-c
---

# --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

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

Find F(1014) (mod 1 000 000 007).

# --hints--

`euler447()` should return 530553372.

```js
assert.strictEqual(euler447(), 530553372);
```

# --seed--

## --seed-contents--

```js
function euler447() {

  return true;
}

euler447();
```

# --solutions--

```js
// solution required
```