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id	title	challengeType	forumTopicId	dashedName
5900f3fa1000cf542c50ff0c	Problem 140: Modified Fibonacci golden nuggets	5	301769	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.

--hints--

euler140() should return 5673835352990.

assert.strictEqual(euler140(), 5673835352990);

--seed--

--seed-contents--

function euler140() {

  return true;
}

euler140();

--solutions--

// solution required

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