# The question is ....

Number Theory Level 5

How many ordered triples $$(a,b,c)$$ are there such that

(i) $$a,b,c$$ are positive, pairwise coprime integers,

(ii) $$a \le b \le c$$, and

(iii) each of $$a,b,c$$ divides the sum of the other two integers?

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