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Date: 12-5-2020
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Date: 21-12-2020
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A triple of positive integers satisfying is said to be geometric if . In particular, such a triple is geometric if its terms form a geometric sequence with common ratio where
One can show that there exists a one-to-one correspondence between the set of equivalence classes of geometric triples and the set of equivalence classes of harmonic triples where here, two triples and are said to be equivalent if , i.e., if there exists some positive real number such that .
REFERENCES:
VanderBurgh, I. (Ed.). "Mathematical Mayhem: Mayhem Solutions." Crux Math. 36, 141-143, 2010.
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