66 lines
1.3 KiB
Markdown
66 lines
1.3 KiB
Markdown
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---
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id: 5
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localeTitle: 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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Para cada entero n> 1, la familia de funciones fn, a, b se define
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por fn, a, b (x) ≡ax + b mod n para a, b, x entero y 0 <a<n, 0≤b<n, 0≤x<n.<code> 0 Llamaremos retracción de fn, a, ba si fn, a, b (fn, a, b (x)) ≡fn, a, b (x) mod n para cada 0≤x <n.<code> 0 Sea R (n) el número de retracciones para n.
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Se le da que
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∑ R (c) para c = C (100 000, k), y 1 ≤ k ≤99 999 ≡628701600 (mod 1 000 000 007).
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(C (n, k) es el coeficiente binomial).
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Encuentre ∑ R (c) para c = C (10 000 000, k), y 1 ≤k≤ 9 999 999.
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Dé su respuesta módulo 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> debe devolver 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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