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Project Euler 71: Listing reduced proper fractions in ascending order of size.
Problem Description
Consider the fraction, n/d, where n and d are positive integers. If n<d and GCD(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 2/5 is the fraction immediately to the left of 3/7.
By listing the set of reduced proper fractions for d ≤ 1,000,000 in ascending order of size, find the numerator of the fraction immediately to the left of 3/7.
Analysis
The answer will always be very close to 3/7*limit. In this case 3/7*1000000 = 428571
Project Euler 71 Solution
Runs < 0.001 seconds in Python 2.7.
Use this link to get the Project Euler 71 Solution Python 2.7 source.
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