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gikf 7907f62337 fix(curriculum): clean-up Project Euler 121-140 (#42731)
* fix: clean-up Project Euler 121-140

* fix: corrections from review

Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com>

* fix: missing backticks

Co-authored-by: Kristofer Koishigawa <scissorsneedfoodtoo@gmail.com>

* fix: corrections from review

Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>

* fix: missing delimiter

Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com>
Co-authored-by: Kristofer Koishigawa <scissorsneedfoodtoo@gmail.com>
Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
2021-07-16 21:38:37 +02:00

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id, title, challengeType, forumTopicId, dashedName
id title challengeType forumTopicId dashedName
5900f3f51000cf542c50ff08 Problem 137: Fibonacci golden nuggets 5 301765 problem-137-fibonacci-golden-nuggets

--description--

Consider the infinite polynomial series A_{F}(x) = xF_1 + x^2F_2 + x^3F_3 + \ldots, where F_k is the $k$th term in the Fibonacci sequence: 1, 1, 2, 3, 5, 8, \ldots; that is, F_k = F_{k 1} + F_{k 2}, F_1 = 1 and F_2 = 1.

For this problem we shall be interested in values of x for which A_{F}(x) is a positive integer.

Surprisingly

$$\begin{align} A_F(\frac{1}{2}) & = (\frac{1}{2}) × 1 + {(\frac{1}{2})}^2 × 1 + {(\frac{1}{2})}^3 × 2 + {(\frac{1}{2})}^4 × 3 + {(\frac{1}{2})}^5 × 5 + \cdots \\ & = \frac{1}{2} + \frac{1}{4} + \frac{2}{8} + \frac{3}{16} + \frac{5}{32} + \cdots \\ & = 2 \end{align}$$

The corresponding values of x for the first five natural numbers are shown below.

x A_F(x)
\sqrt{2} 1 1
\frac{1}{2} 2
\frac{\sqrt{13} 2}{3} 3
\frac{\sqrt{89} 5}{8} 4
\frac{\sqrt{34} 3}{5} 5

We shall call A_F(x) a golden nugget if x is rational, because they become increasingly rarer; for example, the 10th golden nugget is 74049690.

Find the 15th golden nugget.

--hints--

goldenNugget() should return 1120149658760.

assert.strictEqual(goldenNugget(), 1120149658760);

--seed--

--seed-contents--

function goldenNugget() {

  return true;
}

goldenNugget();

--solutions--

// solution required