Significance of a polynomial
\[\large f(1)=f(2)=f(3) = \ldots = f(4535) = f(4536)=0\]
If \(f(x)\) is a monic polynomial of degree 4537, such that the equation above is satisfied and that \( f( 4537) - f(0) = N ! \) where \(N\) is a positive integer, what is \(N\)?
Bonus: Can you generalize this?