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.
by
Calvin Lin