# Divisibility #1

A polynomial $f(x)$ satisfies the following conditions:

• $\displaystyle \lim_{x \to \infty} \frac{f(x)}{x^2} = 1$
• $f(-1) > 1$
• $f(0)$ is a prime number
• There exists an integer $k > 1$ such that for all positive integer $n$, $f(n)$ is a positive integer divisible by $k$

Find the maximum value of $f(1) + k$.

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