project_euler.problem_044.sol1
==============================

.. py:module:: project_euler.problem_044.sol1

.. autoapi-nested-parse::

   Problem 44: https://projecteuler.net/problem=44

   Pentagonal numbers are generated by the formula, Pn=n(3n-1)/2. The first ten
   pentagonal numbers are:
   1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...
   It can be seen that P4 + P7 = 22 + 70 = 92 = P8. However, their difference,
   70 - 22 = 48, is not pentagonal.

   Find the pair of pentagonal numbers, Pj and Pk, for which their sum and difference
   are pentagonal and D = |Pk - Pj| is minimised; what is the value of D?



Functions
---------

.. autoapisummary::

   project_euler.problem_044.sol1.is_pentagonal
   project_euler.problem_044.sol1.solution


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

.. py:function:: is_pentagonal(n: int) -> bool

   Returns True if n is pentagonal, False otherwise.
   >>> is_pentagonal(330)
   True
   >>> is_pentagonal(7683)
   False
   >>> is_pentagonal(2380)
   True


.. py:function:: solution(limit: int = 5000) -> int

   Returns the minimum difference of two pentagonal numbers P1 and P2 such that
   P1 + P2 is pentagonal and P2 - P1 is pentagonal.
   >>> solution(5000)
   5482660