---
id: 5900f3fa1000cf542c50ff0c
challengeType: 5
title: 'Problem 140: Modified Fibonacci golden nuggets'
---

## Description
<section id='description'>
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, ... .
For this problem we shall be concerned with values of x for which AG(x) is a positive integer.
The corresponding values of x for the first five natural numbers are shown below.

xAG(x)
(√5−1)/41
2/52
(√22−2)/63
(√137−5)/144
1/25

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.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler140()</code> should return 5673835352990.
    testString: assert.strictEqual(euler140(), 5673835352990, '<code>euler140()</code> should return 5673835352990.');

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler140() {
  // Good luck!
  return true;
}

euler140();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>
