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>
77 lines
1.4 KiB
Markdown
77 lines
1.4 KiB
Markdown
---
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id: 5900f5241000cf542c510036
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challengeType: 5
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isHidden: false
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title: 'Problem 437: Fibonacci primitive roots'
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forumTopicId: 302108
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---
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## Description
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<section id='description'>
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When we calculate 8n modulo 11 for n=0 to 9 we get: 1, 8, 9, 6, 4, 10, 3, 2, 5, 7.
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As we see all possible values from 1 to 10 occur. So 8 is a primitive root of 11.
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But there is more:
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If we take a closer look we see:
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1+8=9
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8+9=17≡6 mod 11
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9+6=15≡4 mod 11
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6+4=10
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4+10=14≡3 mod 11
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10+3=13≡2 mod 11
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3+2=5
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2+5=7
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5+7=12≡1 mod 11.
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So the powers of 8 mod 11 are cyclic with period 10, and 8n + 8n+1 ≡ 8n+2 (mod 11).
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8 is called a Fibonacci primitive root of 11.
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Not every prime has a Fibonacci primitive root.
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There are 323 primes less than 10000 with one or more Fibonacci primitive roots and the sum of these primes is 1480491.
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Find the sum of the primes less than 100,000,000 with at least one Fibonacci primitive root.
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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>euler437()</code> should return 74204709657207.
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testString: assert.strictEqual(euler437(), 74204709657207);
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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 euler437() {
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// Good luck!
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return true;
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}
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euler437();
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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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