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>
83 lines
1.6 KiB
Markdown
83 lines
1.6 KiB
Markdown
---
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id: 5900f3b11000cf542c50fec4
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challengeType: 5
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isHidden: false
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title: 'Problem 69: Totient maximum'
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forumTopicId: 302181
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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 numbers less than <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.
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<div style='margin-left: 4em;'>
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|<var>n</var>|Relatively Prime|φ(<var>n</var>)|<var>n</var>/φ(<var>n</var>)|
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|--- |--- |--- |--- |
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|2|1|1|2|
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|3|1,2|2|1.5|
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|4|1,3|2|2|
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|5|1,2,3,4|4|1.25|
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|6|1,5|2|3|
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|7|1,2,3,4,5,6|6|1.1666...|
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|8|1,3,5,7|4|2|
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|9|1,2,4,5,7,8|6|1.5|
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|10|1,3,7,9|4|2.5|
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</div>
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It can be seen that <var>n</var>=6 produces a maximum <var>n</var>/φ(<var>n</var>) for <var>n</var> ≤ 10.
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Find the value of <var>n</var> ≤ 1,000,000 for which n/φ(<var>n</var>) is a maximum.
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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>totientMaximum()</code> should return a number.
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testString: assert(typeof totientMaximum() === 'number');
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- text: <code>totientMaximum()</code> should return 510510.
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testString: assert.strictEqual(totientMaximum(), 510510);
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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 totientMaximum() {
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// Good luck!
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return true;
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}
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totientMaximum();
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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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