project_euler.problem_137.sol1
==============================

.. py:module:: project_euler.problem_137.sol1

.. autoapi-nested-parse::

   Project Euler Problem 137: https://projecteuler.net/problem=137

   Fibonacci Golden Nuggets

   The polynomial sequence can be rewritten in the finite form:

   A_F(x) = x / (1 - x - x^2)

   And then the problem is to solve for it for rational x that give A_F(x) as positive
   integer. It turns out that the solution is for the n-th golden nugget is given by
   F(2n) * F(2n + 1), where F(k) is the k'th Fibonacci number.

   Reference: https://oeis.org/A081018



Functions
---------

.. autoapisummary::

   project_euler.problem_137.sol1.solution


Module Contents
---------------

.. py:function:: solution(n: int = 15) -> int

   It calculates fibonachi numbers 2n and 2n+1, and returns their product.

   >>> solution(3)
   104
   >>> solution(10)
   74049690