Find the number of pairwise coprime triples of positive integers (a,b,c) with a<b<c such that
a∣bc−31,b∣ca−31 and c∣ab−31.
Details and assumptions
The notation n∣m means that n is a divisor of m.
Clarification: (ab−31),(ac−31), and (bc−31) may be zero or negative.