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Geometric Triple

المؤلف:  VanderBurgh, I. (Ed.).

المصدر:  "Mathematical Mayhem: Mayhem Solutions." Crux Math. 36

الجزء والصفحة:  ...

27-10-2020

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Geometric Triple

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.