# Define a polynomial $$f(x) = (x-a)(x-b)(x-c)$$

$\large a + b + c + ab + bc + ac = abc + 1$

Determine the number of triplets of positive integers $$(a,b,c)$$ with $$c\geq b \geq a$$ such that the equation above is fulfilled.

##### This problem appeared in RMO 2005.(#6)
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