Given 3 positive integers p,q and b, where p and q represent the numerator
and denominator of a rational number (respectively), and b a numerical
base (or radix), how can we know if p%q has a finite (or not)
representation in b?  

In other words, if p%q can be represented by a finite
(non-infinitely-repeating) decimal in base b, then what do we know about
the relationship of p to q or p%q to b ?

You may allow p to take on the value 0 if needed for generality, but q is
strictly > 0 (obviously) and b is strictly > 1 (probably?).

-Dan

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