# Coprime Triples

Find the number of pairwise coprime triples of positive integers $$(a,b,c)$$ with $$a < b < c$$ such that

$a| bc-31, b|ca-31 \mbox{ and }c|ab-31.$

Details and assumptions

The notation $$n \mid m$$ means that $$n$$ is a divisor of $$m$$.

Clarification: $$(ab-31), (ac-31),$$ and $$(bc-31)$$ may be zero or negative.

×