project_euler.problem_129.sol1
==============================

.. py:module:: project_euler.problem_129.sol1

.. autoapi-nested-parse::

   Project Euler Problem 129: https://projecteuler.net/problem=129

   A number consisting entirely of ones is called a repunit. We shall define R(k) to be
   a repunit of length k; for example, R(6) = 111111.

   Given that n is a positive integer and GCD(n, 10) = 1, it can be shown that there
   always exists a value, k, for which R(k) is divisible by n, and let A(n) be the least
   such value of k; for example, A(7) = 6 and A(41) = 5.

   The least value of n for which A(n) first exceeds ten is 17.

   Find the least value of n for which A(n) first exceeds one-million.



Functions
---------

.. autoapisummary::

   project_euler.problem_129.sol1.least_divisible_repunit
   project_euler.problem_129.sol1.solution


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

.. py:function:: least_divisible_repunit(divisor: int) -> int

   Return the least value k such that the Repunit of length k is divisible by divisor.
   >>> least_divisible_repunit(7)
   6
   >>> least_divisible_repunit(41)
   5
   >>> least_divisible_repunit(1234567)
   34020


.. py:function:: solution(limit: int = 1000000) -> int

   Return the least value of n for which least_divisible_repunit(n)
   first exceeds limit.
   >>> solution(10)
   17
   >>> solution(100)
   109
   >>> solution(1000)
   1017