# 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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