project_euler.problem_072.sol2
==============================

.. py:module:: project_euler.problem_072.sol2

.. autoapi-nested-parse::

   Project Euler Problem 72: https://projecteuler.net/problem=72

   Consider the fraction, n/d, where n and d are positive integers. If n<d and HCF(n,d)=1,
   it is called a reduced proper fraction.

   If we list the set of reduced proper fractions for d ≤ 8 in ascending order of size,
   we get:

   1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2,
   4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8

   It can be seen that there are 21 elements in this set.

   How many elements would be contained in the set of reduced proper fractions
   for d ≤ 1,000,000?



Functions
---------

.. autoapisummary::

   project_euler.problem_072.sol2.solution


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

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

   Return the number of reduced proper fractions with denominator less than limit.
   >>> solution(8)
   21
   >>> solution(1000)
   304191