79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
65 lines
1.0 KiB
Markdown
65 lines
1.0 KiB
Markdown
---
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id: 5900f52c1000cf542c51003d
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challengeType: 5
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title: 'Problem 446: Retractions B'
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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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F(N)=∑R(n4+4) for 1≤n≤N.
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F(1024)=77532377300600.
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Find F(107) (mod 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>euler446()</code> should return 907803852.
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testString: assert.strictEqual(euler446(), 907803852, '<code>euler446()</code> should return 907803852.');
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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 euler446() {
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// Good luck!
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return true;
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}
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euler446();
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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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