70 lines
1.3 KiB
Markdown
70 lines
1.3 KiB
Markdown
---
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id: 5900f3fa1000cf542c50ff0c
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challengeType: 5
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title: 'Problem 140: Modified Fibonacci golden nuggets'
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forumTopicId: 301769
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---
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## Description
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<section id='description'>
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Consider the infinite polynomial series AG(x) = xG1 + x2G2 + x3G3 + ..., where Gk is the kth term of the second order recurrence relation Gk = Gk−1 + Gk−2, G1 = 1 and G2 = 4; that is, 1, 4, 5, 9, 14, 23, ... .
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For this problem we shall be concerned with values of x for which AG(x) is a positive integer.
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The corresponding values of x for the first five natural numbers are shown below.
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xAG(x)
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(√5−1)/41
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2/52
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(√22−2)/63
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(√137−5)/144
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1/25
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We shall call AG(x) a golden nugget if x is rational, because they become increasingly rarer; for example, the 20th golden nugget is 211345365.
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Find the sum of the first thirty golden nuggets.
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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>euler140()</code> should return 5673835352990.
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testString: assert.strictEqual(euler140(), 5673835352990);
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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 euler140() {
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// Good luck!
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return true;
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}
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euler140();
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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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