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no of harmonic triples (a, b, c) is equal to the no of positive divisor of c^2

Source: 2001 Estonia National Olympiad Final Round grade 10 p4

March 12, 2020

number theoryharmonicDivisors

Problem Statement

We call a triple of positive integers

(a, b, c)

harmonic if

\frac{1}{a}=\frac{1}{b}+\frac{1}{c}

. Prove that, for any given positive integer

c

, the number of harmonic triples

(a, b, c)

is equal to the number of positive divisors of

c^2