A triple 
of positive integers satisfying 
is said to be harmonic if
 |
In particular, such a triple is harmonic if the reciprocals of its terms form an arithmetic sequence with
common difference 
where
 |
One can show that there exists a one-to-one correspondence between the set of equivalence
classes of harmonic triples and the set of equivalence classes of geometric
triples where here, two triples 
and 
are said to be equivalent
if 
,
i.e., if there exists some positive real
number 
such that 
.
