Feat: add new Markdown parser (#39800)

and change all the challenges to new `md` format.
This commit is contained in:
Oliver Eyton-Williams
2020-11-27 19:02:05 +01:00
committed by GitHub
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commit 0bd52f8bd1
2580 changed files with 113436 additions and 111979 deletions

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---
id: 5900f52a1000cf542c51003c
challengeType: 5
title: 'Problem 445: Retractions A'
challengeType: 5
forumTopicId: 302117
---
## 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, 0b<n, 0x<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 0x<n.
Let R(n) be the number of retractions for n.
# --description--
For every integer n>1, the family of functions fn,a,b is defined
You are given that
R(c) for c=C(100 000,k), and 1 k 99 999 628701600 (mod 1 000 000 007).
(C(n,k) is the binomial coefficient).
by fn,a,b(x)≡ax+b mod n for a,b,x integer and 0
Find R(c) for c=C(10 000 000,k), and 1 k 9 999 999.
Give your answer modulo 1 000 000 007.
</section>
You are given that ∑ R(c) for c=C(100 000,k), and 1 ≤ k ≤99 999 ≡628701600 (mod 1 000 000 007). (C(n,k) is the binomial coefficient).
## Instructions
<section id='instructions'>
Find ∑ R(c) for c=C(10 000 000,k), and 1 ≤k≤ 9 999 999. Give your answer modulo 1 000 000 007.
</section>
# --hints--
## Tests
<section id='tests'>
```yml
tests:
- text: <code>euler445()</code> should return 659104042.
testString: assert.strictEqual(euler445(), 659104042);
`euler445()` should return 659104042.
```js
assert.strictEqual(euler445(), 659104042);
```
</section>
# --seed--
## Challenge Seed
<section id='challengeSeed'>
<div id='js-seed'>
## --seed-contents--
```js
function euler445() {
@ -52,17 +36,8 @@ function euler445() {
euler445();
```
</div>
</section>
## Solution
<section id='solution'>
# --solutions--
```js
// solution required
```
</section>