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Find the number of ordered triples of positive integers (a,b,c)(a,b,c)(a,b,c) that satisfy the equation abc−ab−bc−ca+a+b+c=2013\displaystyle abc-ab-bc-ca+a+b+c=2013abc−ab−bc−ca+a+b+c=2013
Extras:
This is in the set Contest Problems.
This is from PUMaC.
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