Find the largest possible integer \(n\) such that there exists a non-constant quadratic polynomial \(f(x)\) with integer coefficients satisfying

\[ f(1) \mid f(2), f(2) \mid f(3), \ldots f(n−1) \mid f(n).\]

**Details and assumptions**

For (possibly negative or zero) integers \(m\) and \(k\) the notation \(m \mid k\) means that \(k=m\cdot i\) for some integer \(i.\)

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