project_euler.problem_072.sol2

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

solution(→ int)

Return the number of reduced proper fractions with denominator less than limit.

Module Contents

project_euler.problem_072.sol2.solution(limit: int = 1000000) → int

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