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

**Number Theory**Level 4

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

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