71 lines
1.2 KiB
Markdown
71 lines
1.2 KiB
Markdown
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---
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id: 5900f5311000cf542c510042
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challengeType: 5
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title: 'Problem 451: Modular inverses'
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---
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## Description
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<section id='description'>
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Consider the number 15.
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There are eight positive numbers less than 15 which are coprime to 15: 1, 2, 4, 7, 8, 11, 13, 14.
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The modular inverses of these numbers modulo 15 are: 1, 8, 4, 13, 2, 11, 7, 14
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because
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1*1 mod 15=1
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2*8=16 mod 15=1
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4*4=16 mod 15=1
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7*13=91 mod 15=1
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11*11=121 mod 15=1
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14*14=196 mod 15=1
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Let I(n) be the largest positive number m smaller than n-1 such that the modular inverse of m modulo n equals m itself.
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So I(15)=11.
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Also I(100)=51 and I(7)=1.
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Find ∑I(n) for 3≤n≤2·107
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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>euler451()</code> should return 153651073760956.
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testString: 'assert.strictEqual(euler451(), 153651073760956, ''<code>euler451()</code> should return 153651073760956.'');'
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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 euler451() {
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// Good luck!
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return true;
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}
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euler451();
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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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