freeCodeCamp/curriculum/challenges/en/08-coding-interview-prep/project-euler/problem-140-modified-fibonacci-golden-nuggets.en.md

id, challengeType, title

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

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.

Instructions

Tests

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

Challenge Seed

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

euler140();

Solution

// solution required