47 lines
1.1 KiB
Markdown
47 lines
1.1 KiB
Markdown
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---
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id: 5900f3fa1000cf542c50ff0c
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title: 'Problem 140: Modified Fibonacci golden nuggets'
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challengeType: 5
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forumTopicId: 301769
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dashedName: problem-140-modified-fibonacci-golden-nuggets
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---
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# --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) (√5−1)/41 2/52 (√22−2)/63 (√137−5)/144 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. Find the sum of the first thirty golden nuggets.
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# --hints--
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`euler140()` should return 5673835352990.
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```js
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assert.strictEqual(euler140(), 5673835352990);
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```
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# --seed--
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## --seed-contents--
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```js
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function euler140() {
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return true;
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}
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euler140();
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```
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# --solutions--
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```js
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// solution required
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```
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