79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
67 lines
1.2 KiB
Markdown
67 lines
1.2 KiB
Markdown
---
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id: 5900f52a1000cf542c51003c
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challengeType: 5
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title: 'Problem 445: Retractions A'
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---
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## Description
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<section id='description'>
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For every integer n>1, the family of functions fn,a,b is defined
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by fn,a,b(x)≡ax+b mod n for a,b,x integer and 0<a<n, 0≤b<n, 0≤x<n.
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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.
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Let R(n) be the number of retractions for n.
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You are given that
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∑ R(c) for c=C(100 000,k), and 1 ≤ k ≤99 999 ≡628701600 (mod 1 000 000 007).
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(C(n,k) is the binomial coefficient).
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Find ∑ R(c) for c=C(10 000 000,k), and 1 ≤k≤ 9 999 999.
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Give your answer modulo 1 000 000 007.
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>euler445()</code> should return 659104042.
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testString: assert.strictEqual(euler445(), 659104042, '<code>euler445()</code> should return 659104042.');
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function euler445() {
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// Good luck!
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return true;
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}
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euler445();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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