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?

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