Problem 73: Counting fractions in a range
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 3 fractions between 1/3 and 1/2.
How many fractions lie between 1/3 and 1/2 in the sorted set of reduced proper
fractions for d
≤ 12,000?
Test
{{test}}Console output