Let be the set of all fractions in reduced form lying strictly below 0 and 1 whose denominator is less than or equal to 99. In other words,

where denotes the *greatest common divisor* (or
*highest common factor*) of and .

For instance, includes fractions such as , and and excludes fractions such as , (both not in reduced form) and (denominator too large).

Madhavan Mukund 2003-05-22

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