The number of bases in which 
is a repeating decimal (actually, repeating b-ary) of length l is the same as the number of fractions 
,
,
which have reduced denominator l. For example, in bases 2, 3, ..., 6, 1/7 is given by
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which have periods 3, 6, 3, 6, and 2, respectively, corresponding to the denominators 6, 3, 2, 3, and 6 of
Cyclic Number, Repeating Decimal, Totient Function
