Should have done this 6 years back!

Algebra Level 4

Let \(P(x)\) be a polynomial with degree 2009 and leading co-efficient unity such that

\(P ( 0 ) = 2008, P ( 1 ) = 2007, P ( 2 ) = 2006, . . . . . . . . , P ( 2008 ) = 0 \)

and the value of \(P(2009) = (n!) - a\) where \(n\) and \(a\) are natural numbers, then the value of \(n+a\) is ?

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