MathDB

Let

S

be the set of all rational numbers

r

0<r<1

, that have a repeating decimal expansion in the form

0.abcabcabc\ldots=0.\overline{abc},

where the digits

a

b

, and

c

are not necessarily distinct. To write the elements of

S

as fractions in lowest terms, how many different numerators are required?

5