# Significance of a polynomial

Algebra Level 3

$\large f(1)=f(2)=f(3) = \ldots = f(4535) = f(4536)=0$

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?

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