22afc2a0ca
Co-authored-by: Oliver Eyton-Williams <ojeytonwilliams@gmail.com> Co-authored-by: Kristofer Koishigawa <scissorsneedfoodtoo@gmail.com> Co-authored-by: Beau Carnes <beaucarnes@gmail.com>
67 lines
1.5 KiB
Markdown
67 lines
1.5 KiB
Markdown
---
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id: 5900f3b21000cf542c50fec5
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challengeType: 5
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isHidden: false
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title: 'Problem 70: Totient permutation'
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forumTopicId: 302183
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---
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## Description
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<section id='description'>
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Euler's Totient function, φ(<var>n</var>) [sometimes called the phi function], is used to determine the number of positive numbers less than or equal to <var>n</var> which are relatively prime to <var>n</var>. For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and relatively prime to nine, φ(9)=6. The number 1 is considered to be relatively prime to every positive number, so φ(1)=1.
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Interestingly, φ(87109)=79180, and it can be seen that 87109 is a permutation of 79180.
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Find the value of <var>n</var>, 1 < <var>n</var> < 10<sup>7</sup>, for which φ(<var>n</var>) is a permutation of <var>n</var> and the ratio <var>n</var>/φ(<var>n</var>) produces a minimum.
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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>totientPermutation()</code> should return a number.
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testString: assert(typeof totientPermutation() === 'number');
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- text: <code>totientPermutation()</code> should return 8319823.
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testString: assert.strictEqual(totientPermutation(), 8319823);
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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 totientPermutation() {
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// Good luck!
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return true;
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}
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totientPermutation();
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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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