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curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-447-retractions-c.md

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+---
+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>