Coprime Triples

Number Theory Level 5

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.


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