78 lines
1.4 KiB
Markdown
78 lines
1.4 KiB
Markdown
---
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id: 5900f50d1000cf542c51001f
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challengeType: 5
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title: 'Problem 417: Reciprocal cycles II'
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---
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## Description
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<section id='description'>
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A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:
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1/2= 0.5
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1/3= 0.(3)
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1/4= 0.25
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1/5= 0.2
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1/6= 0.1(6)
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1/7= 0.(142857)
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1/8= 0.125
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1/9= 0.(1)
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1/10= 0.1
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Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.
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Unit fractions whose denominator has no other prime factors than 2 and/or 5 are not considered to have a recurring cycle.
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We define the length of the recurring cycle of those unit fractions as 0.
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Let L(n) denote the length of the recurring cycle of 1/n.
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You are given that ∑L(n) for 3 ≤ n ≤ 1 000 000 equals 55535191115.
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Find ∑L(n) for 3 ≤ n ≤ 100 000 000
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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>euler417()</code> should return 446572970925740.
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testString: 'assert.strictEqual(euler417(), 446572970925740, "<code>euler417()</code> should return 446572970925740.");'
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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 euler417() {
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// Good luck!
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return true;
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}
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euler417();
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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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