project_euler.problem_137.sol1

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

solution(→ int)

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

Module Contents

project_euler.problem_137.sol1.solution(n: int = 15) → int

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

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